International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171110Hybrid function projective synchronization in discrete dynamical networks via adaptive control55935607http://dx.doi.org/10.22436/jnsa.010.11.01ENGhada Al-mahbashiSchool of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, MalaysiaM. S. Md NooraniSchool of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, MalaysiaSakhinah Abu BakarSchool of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, MalaysiaIn this paper, we study the hybrid function projective synchronization between coupled complex discrete networks with different dimensions.
The hybrid function projective synchronization is achieved by designing an adaptive control method. Based on the designed controller and the Lyapunov stability theory, we derive sufficient conditions to realize the hybrid function projective synchronization with different nodes. Moreover, with the adaptive update law, an adaptive control gains are obtained. Furthermore, we examine different cases of outer coupling matrix of node dynamics. Finally, we provide numerical examples to show the effectiveness of the proposed control scheme.http://www.isr-publications.com/jnsa/6067/download-hybrid-function-projective-synchronization-in-discrete-dynamical-networks-via-adaptive-controlInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171110Anti-synchronization of fractional-order chaotic complex systems with unknown parameters via adaptive control56085621http://dx.doi.org/10.22436/jnsa.010.11.02ENCuimei JiangSchool of Science, Qilu University of Technology, Jinan, Shandong 250353, P. R. ChinaFangfang ZhangSchool of Electrical Engineering and Automation, Qilu University of Technology, Jinan, Shandong 250353, P. R. ChinaHaiyong QinSchool of Mathematics, Qilu Normal University, Jinan, Shandong 250013, P. R. ChinaTongxing LiSchool of Information Science and Engineering, Linyi University, Linyi, Shandong 276005, P. R. ChinaThis paper is concerned with adaptive control for anti-synchronization of a class of uncertain fractional-order chaotic complex systems described by a unified mathematical expression.
By utilizing the recently established result for the Caputo fractional derivative of a quadratic function
and employing the adaptive control technique, we design controllers and some fractional-order
parameter update laws
to anti-synchronize two fractional-order chaotic complex systems with unknown parameters.
The proposed method has generality, simplicity, and feasibility.
Moreover, anti-synchronization between uncertain fractional-order complex Lorenz system and fractional-order complex Lu system is implemented as an example to demonstrate the effectiveness and feasibility of the proposed scheme.http://www.isr-publications.com/jnsa/6068/download-anti-synchronization-of-fractional-order-chaotic-complex-systems-with-unknown-parameters-via-adaptive-controlInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171110The stochastic interactions between predator and prey under Markovian switching: competitive interaction between multiple prey56225645http://dx.doi.org/10.22436/jnsa.010.11.03ENYanqing LiCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. ChinaLong ZhangCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. ChinaIn this paper, a class of
predator-prey model with prey competition is proposed, in which the interactions of predation between predator and prey are randomised and subsequently evaluated under Markovian switching. By constructing appropriate Lyapunov functions and applying various analytical methods, sufficient conditions for the existence of unique global positive solution, stochastic permanence and mean extinction are established. In the permanence case, we also estimate the superior and inferior limits of the sample path in a time-averaged Markov decision. We conclude that the interactions between predator and two prey, two competitive prey themselves and the dynamical properties of switching subsystems are not only dependent on subsystem coefficients but also on the transition probability of the Markov chain (switching from one state to another). Specific examples and numerical simulations are provided to demonstrate our theoretical results.http://www.isr-publications.com/jnsa/6069/download-the-stochastic-interactions-between-predator-and-prey-under-markovian-switching-competitive-interaction-between-multiple-preyInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171110Robustness analysis of global exponential stability in neural networks evoked by deviating argument and stochastic disturbance56465667http://dx.doi.org/10.22436/jnsa.010.11.04ENLiguang WanCollege of Mechatronics and Control Engineering, Hubei Normal University, Huangshi 435002, ChinaAilong WuCollege of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, ChinaJingru ChenDepartment of Personnel, Hubei Normal University, Huangshi 435002, ChinaThis paper studies the robustness of global exponential stability of
neural networks evoked by deviating argument and stochastic
disturbance. Given the original neural network is globally
exponentially stable, we discuss the problem that the neural network
is still globally exponentially stable when the deviating argument
or both the deviating argument and stochastic disturbance is/are
generated. By virtue of solving the derived transcendental
equation(s), the upper bound(s) about the intensity of the deviating
argument or both of the deviating argument and stochastic
disturbance is/are received. The obtained theoretical results are
the supplements to the existing literatures on global exponential
stability of neural networks. Two numerical examples are offered to
demonstrate the effectiveness of theoretical results.http://www.isr-publications.com/jnsa/6070/download-robustness-analysis-of-global-exponential-stability-in-neural-networks-evoked-by-deviating-argument-and-stochastic-disturbanceInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171110Some fixed point theorems for \(\varphi\)-contractive mappings in fuzzy normed linear spaces56685676http://dx.doi.org/10.22436/jnsa.010.11.05ENSorinNădăbanDepartment of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Dragoi 2, RO-310330, Arad, RomaniaTudorBînzarDepartment of Mathematics, Politehnica University of Timisoara, Regina Maria 1, RO-300004, Timisoara, RomaniaFlavius PaterDepartment of Mathematics, Politehnica University of Timisoara, Regina Maria 1, RO-300004, Timisoara, RomaniaIn this paper a new concept of comparison function is introduced and discussed and some fixed point theorems are established for \(\varphi\)-contractive mappings in fuzzy normed linear spaces. In this way we obtain fuzzy versions of some classical fixed point theorems such as Nemytzki-Edelstein's theorem and Maia's theorem. http://www.isr-publications.com/jnsa/6071/download-some-fixed-point-theorems-for-varphi-contractive-mappings-in-fuzzy-normed-linear-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171110Study on differentiability problems of interval-valued functions56775689http://dx.doi.org/10.22436/jnsa.010.11.06ENYu-E BaoCollege of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia 028043, P. R. ChinaJin-Jun Li College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia 028043, P. R. ChinaEer-Dun BaiCollege of Computer Science and Technology, Inner Mongolia Universities, Tongliao, Inner Mongolia 028043, P. R. ChinaIn this paper, we give the concepts of \(H\)-directional differentiability and \(D\)-directional differentiability of interval-valued functions. Then we discuss the properties of \(H\)-directional differentiable interval-valued functions and \(D\)-directional differentiable interval-valued functions. The necessary and sufficient conditions for the \(H\)-directional differentiability are given together with the sufficient conditions and the necessary and sufficient conditions for \(D\)-directional differentiability of interval-valued functions. Then we discuss the relationship between the two directional differentiability and prove these directional differentiability can be equivalent under a certain conditions.http://www.isr-publications.com/jnsa/6072/download-study-on-differentiability-problems-of-interval-valued-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Fixed points of weakly compatible mappings satisfying a generalized common limit range property56905700http://dx.doi.org/10.22436/jnsa.010.11.07ENAziz KhanDepartment of Mathematics, University of Peshawar, P. O. Box 25000, Khyber Pakhtunkhwa, PakistanHasib KhanCollege of Engineering, Mechanics and Materials, Hohai University, 210098, Nanjing, P. R. ChinaDumitru BaleanuDepartment of Mathematics, Cankaya University, 06530 Ankara, TurkeyErdal KarapinarDepartment of Mathematics, Atilim University, 06586 Incek, Ankara, TurkeyTahir Saeed KhanDepartment of Mathematics, University of Peshawar, P. O. Box 25000, Khyber Pakhtunkhwa, PakistanIn this paper, we produce new fixed point theorems for \(2n\) self-mappings \(\wp^a_1,\wp^a_2,\ldots,\wp^a_n\), \(\gamma^b_1,\gamma^b_2,\ldots,\gamma^b_n:\mathcal{X}\rightarrow\mathcal{X}\) on a metric space \((\mathcal{X},\rho )\), satisfying a generalized common limit range (CLR) property or CLR\(_{\wp^a_k\gamma^b_l}\) for \(k,l=2,\ldots,n\). Along with the newly introduced property CLR\(_{\wp^a_k\gamma^b_l}\) for \(k,l=2,\ldots,n\) for the \(2n\) self-mappings, we also assume that the pairs \((\wp^a_1,\gamma^b_1),(\wp^a_2,\gamma^b_2),\ldots,(\wp^a_n,\gamma^b_n)\) are weakly compatible. From the main result, we produce three more corollaries as its special cases. These results generalize the work of Sarwar et al. [M. Sarwar, M. Bahadur Zada, I. M. Erhan, Fixed Point Theory Appl., \({\bf 2015}\) (2015), 15 pages] and many others in the available literature. Two examples are also presented for the applications of our new FPTs.http://www.isr-publications.com/jnsa/6096/download-fixed-points-of-weakly-compatible-mappings-satisfying-a-generalized-common-limit-range-propertyInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Hyers-Ulam stability of nonlinear impulsive Volterra integro-delay dynamic system on time scales57015711http://dx.doi.org/10.22436/jnsa.010.11.08ENAkbar ZadaDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanSyed Omar ShahDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanYongjin LiDepartment of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P. R. ChinaThis paper proves the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of nonlinear impulsive Volterra integro-delay dynamic system on time scales via a fixed point approach. The uniqueness and existence of the solution of nonlinear impulsive Volterra integro-delay dynamic system is proved with the help of Picard operator. The main tools for proving our results are abstract Gronwall lemma and Banach contraction principle. We also make some assumptions along with Lipschitz condition which make our results appropriate for the approach we are
using.http://www.isr-publications.com/jnsa/6097/download-hyers-ulam-stability-of-nonlinear-impulsive-volterra-integro-delay-dynamic-system-on-time-scalesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Viscosity regularization iterative methods and convergence analysis57125722http://dx.doi.org/10.22436/jnsa.010.11.09ENDongfeng LiSchool of Information Engineering, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaJuan ZhaoSchool of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaIn this paper, a Moudafi's type viscosity regularization iterative method is introduced and investigated for an \(m\)-accretive mapping and a nonexpansive mapping. Strong convergence of the regularization iterative method is obtained in the framework of real uniformly smooth Banach spaces. Some subresults are also provided as applications of the main results.http://www.isr-publications.com/jnsa/6098/download-viscosity-regularization-iterative-methods-and-convergence-analysisInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Some fixed point theorems for \(\theta\)-\(\phi\) \({C}\)-contractions57235733http://dx.doi.org/10.22436/jnsa.010.11.10ENDingwei ZhengCollege of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. ChinaXinhe LiuCollege of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. ChinaGengrong ZhangCollege of Mathematics and Computationl Science, Hunan First Normal University, Changsha, Hunan, 410205, P. R. ChinaIn this paper, we introduce the notion of \(\theta\)-\(\phi\) \({C}\)-contraction and establish some fixed point and coupled fixed point theorems for these mappings in the setting of complete metric spaces and ordered metric spaces. The results presented in the paper improve and extend some well-known results. Also, we give an example to illustrate them.http://www.isr-publications.com/jnsa/6099/download-some-fixed-point-theorems-for-theta-phi-c-contractionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Solvability of second-order \(m\)-point difference equation boundary value problems on infinite intervals57345743http://dx.doi.org/10.22436/jnsa.010.11.11ENChanglong YuCollege of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. ChinaJufang WangCollege of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. ChinaYanping GuoCollege of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. ChinaSurong MiaoCollege of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. ChinaIn this paper, we study second-order \(m\)-point
difference boundary value problems on infinite intervals
\[
\left\{\begin{array}{l}
\Delta^{2}x(k-1)+f(k,x(k),\Delta x(k-1))=0,~k\in N,\\
x(0)=\sum\limits_{i=1}^{m-2}\alpha_{i}x(\eta_{i}),~\lim\limits_{k
\rightarrow\infty }\Delta x(k)=0,
\end{array}
\right.
\]
where \(N=\{1,2,\cdots\},\ f:N\times R^{2}\rightarrow R\)
is continuous, \(\alpha_{i}\in
R,~\sum\limits_{i=1}^{m-2}\alpha_{i}\neq1,~\eta_{i}\in
N,~0<\eta_{1}<\eta_{2}<\cdots<\infty\) and
\[\Delta x(k)=x(k+1)-x(k),\]
the nonlinear term is dependent in a difference of lower order on
infinite intervals. By using Leray-Schauder continuation theorem,
the existence of solutions are investigated. Finally, we give one
example to demonstrate the use of the main result. http://www.isr-publications.com/jnsa/6100/download-solvability-of-second-order-m-point-difference-equation-boundary-value-problems-on-infinite-intervalsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Existence of solutions for nonlinear Caputo-Hadamard fractional differential equations via the method of upper and lower solutions57445752http://dx.doi.org/10.22436/jnsa.010.11.12ENYunru BaiInstitute of Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Lojasiewicza 6, 30-348 Krakow, PolandHua KongData Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, ChinaThe purpose of this paper is devoted to consider the existence of solutions for a class of nonlinear Caputo-Hadamard fractional differential equations with integral terms ((CHFDE), for short). Firstly, by applying the semi-group property of Hadamard fractional integral operator, a necessary condition of solvability for (CHFDE) is established. Then, under the suitable conditions, we prove the solution set of (CHFDE) is nonempty by using the method of upper and lower solutions, and Arzel\`{a}-Ascoli theorem. Finally, we present several numerical examples to explicate
the main results. http://www.isr-publications.com/jnsa/6101/download-existence-of-solutions-for-nonlinear-caputo-hadamard-fractional-differential-equations-via-the-method-of-upper-and-lower-solutionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Dynamics of a diffusive viral model with Beddington-DeAngelis incidence rate and CTL immune response57535762http://dx.doi.org/10.22436/jnsa.010.11.13ENKejun ZhuangSchool of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, ChinaIn this paper, a four-dimensional system of viral model with cytotoxic lymphocyte (CTL) immune response is investigated. This model is a reaction-diffusion system with
Beddington-DeAngelis incidence rate and free diffusion in a bounded domain. With the help of comparison principle and Lyapunov function method, the well-posedness of solutions and sufficient conditions for global stability of nonnegative equilibria are established. It can be found that free diffusion has no influence on the global stability of the system with homogeneous Neumann boundary conditions.http://www.isr-publications.com/jnsa/6102/download-dynamics-of-a-diffusive-viral-model-with-beddington-deangelis-incidence-rate-and-ctl-immune-responseInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Fixed point theorems in fuzzy cone metric spaces57635769http://dx.doi.org/10.22436/jnsa.010.11.14ENSaif Ur RehmanDepartment of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. ChinaHong-Xu LiDepartment of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. ChinaIn this paper we prove some fixed point theorems in fuzzy cone metric spaces under some fuzzy cone contractive type conditions. Our results generalize the ``fuzzy cone Banach contraction theorem'' given by [T. Oner, M. B. Kandemire, B. Tanay, J. Nonlinear Sci. Appl., \(\textbf{8}\) (2015), 610--616] recently. http://www.isr-publications.com/jnsa/6103/download-fixed-point-theorems-in-fuzzy-cone-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Weighted Simpson type inequalities for \(h\)-convex functions57705780http://dx.doi.org/10.22436/jnsa.010.11.15ENMarian MatłokaDepartment of Applied Mathematics, Poznań University of Economics, Aleja Niepodległości 10, 61-875 Poznań, PolandIn this paper we establish some weighted Simpson type inequalities
for functions whose derivatives in absolute value are \(h\)-convex.http://www.isr-publications.com/jnsa/6104/download-weighted-simpson-type-inequalities-for-h-convex-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115The necessary and sufficient conditions of Hyers-Ulam stability for a class of parabolic equation57815788http://dx.doi.org/10.22436/jnsa.010.11.16ENXiangkui ZhaoSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaXiaojun WuSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaZhihong ZhaoSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaThe aim of this paper is to consider the Hyers-Ulam stability of a class of parabolic equation \[\left\{\begin{array}{ll}
\frac{\partial u}{\partial t}- a^{2}\Delta u+b\cdot\nabla u+cu=0,~~~(x,t)\in\mathbb{R}^{n}\times(0,+\infty),\\
u(x,0)=\varphi(x),~~~x\in\mathbb{R}^{n}.\end{array}\right.\] We conclude that
(i) it is Hyers-Ulam stable on any finite interval;
(ii) if $c\neq0 $, it is Hyers-Ulam stable on the semi-infinite interval;
(iii) if $c=0$, it is not Hyers-Ulam stable on the semi-infinite interval by using Fourier transformation.
Furthermore, our results can be applied to the mean square Hyers-Ulam stability of parabolic equations driven by an \(n\)-dimensional Brownian motion. http://www.isr-publications.com/jnsa/6107/download-the-necessary-and-sufficient-conditions-of-hyers-ulam-stability-for-a-class-of-parabolic-equationInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171115Inequalities via generalized \(\log m\)-convex functions57895802http://dx.doi.org/10.22436/jnsa.010.11.17ENMuhammad Aslam NoorDepartment of Mathematics, COMSATS Institute of Information Technology, Islamabad, PakistanKhalida Inayat NoorDepartment of Mathematics, COMSATS Institute of Information Technology, Islamabad, PakistanFarhat SafdarDepartment of Mathematics, COMSATS Institute of Information Technology, Islamabad, PakistanMuhammad Uzair AwanDepartment of Mathematics, Government College University, Faisalabad, PakistanSaleem UllahDepartment of Mathematics, University of Islamabad, Islamabad, PakistanThe main objective of this paper is to introduce and investigate a new class of
convex functions, which is called as generalized \(\log\)
\(m\)-convex function. Some new Hermite-Hadamard type of integral inequalities
via generalized \(\log\) \(m\)-convex functions are obtained.
Several special cases are also discussed.http://www.isr-publications.com/jnsa/6108/download-inequalities-via-generalized-log-m-convex-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171117Approximation with modified Phillips operators58035812http://dx.doi.org/10.22436/jnsa.010.11.18ENDanyal SoybaşDepartment of Mathematics Education, Faculty of Education, Erciyes University, Kayseri 38039, TurkeyIn the present paper, we study modified Phillips operators in simultaneous approximation. The operators discussed here are important as they have link with the well-known Szász operators. We estimate some direct results for the operators.http://www.isr-publications.com/jnsa/6127/download-approximation-with-modified-phillips-operatorsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171117Asymptotic behavior of solutions to a class of coupled semilinear parabolic systems with gradient terms58135824http://dx.doi.org/10.22436/jnsa.010.11.19ENYang NaSchool of Mathematics, Jilin University, Changchun 130012, P. R. ChinaYuanyuan NieSchool of Mathematics, Jilin University, Changchun 130012, P. R. ChinaXu ZhouCollege of Computer Science and Technology, Jilin University, Changchun 130012, P. R. ChinaThis paper concerns the asymptotic behavior of solutions
to the Cauchy problem of a class of coupled semilinear parabolic systems with gradient terms.
Using the energy comparison method and comparison principle,
the blow-up theorem of Fujita type is established
and the critical Fujita curve is formulated by spacial dimension,
the behavior of the coefficient of the gradient term at infinity.http://www.isr-publications.com/jnsa/6128/download-asymptotic-behavior-of-solutions-to-a-class-of-coupled-semilinear-parabolic-systems-with-gradient-termsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171117Robust weighted expected residual minimization formulation for stochastic vector variational inequalities58255833http://dx.doi.org/10.22436/jnsa.010.11.20ENYong ZhaoCollege of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing 400074, ChinaZai Yun PengCollege of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing 400074, ChinaYun Bin ZhaoSchool of Mathematics, University of Birmingham, Birmingham, UKIn order to deal with (stochastic) multi-objective optimization problems, a robust Pareto optimal solution by minimizing the worst case weighted sum of
objectives on a given weight set is considered [J. Hu, S. Mehrotra, Oper. Res., \(\textbf{60}\) (2011), 936--953], [J. Hu, T. Homem-de-Mello, S. Mehrotra, Manuscript, (2010)]. Based on this idea, we introduce a new class of deterministic model for stochastic vector variational inequalities, called robust weighted expected residual minimization model. Then we propose sample average approximation (SAA) approach to solve robust weighted expected residual minimization problems. Some convergence results are established for the approximation
problem in terms of the optimal value and the set of optimal solutions. http://www.isr-publications.com/jnsa/6129/download-robust-weighted-expected-residual-minimization-formulation-for-stochastic-vector-variational-inequalitiesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171117Stability analysis for a delayed SIR model with a nonlinear incidence rate58345845http://dx.doi.org/10.22436/jnsa.010.11.21ENLuju LiuSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, ChinaYan WangCollege of Science, China University of Petroleum, Qingdao, 266580, ChinaWe develop an SIR vector-bone epidemic model incorporating
incubation time delay and the nonlinear incidence rate, where the
growth of susceptibles is governed by the logistic equation. The
threshold parameter \(R_0\) is used to determine whether the disease
persists in the population. The model always has the trivial
equilibrium and the disease-free equilibrium whereas admits the
endemic equilibrium if \(R_0\) exceeds one. The disease-free
equilibrium is globally asymptotically stable if \(R_0\) is less than
one, while the system is persistent if \(R_0\) is greater than one.
Furthermore, by applying the time delay as a bifurcation parameter,
the local stability of the endemic equilibrium is discussed and it
loses stability and Hopf bifurcation occurs as the length of the
time delay increases past \(\tau_0\) under certain conditions. An
example is carried out to illustrate the main results.http://www.isr-publications.com/jnsa/6130/download-stability-analysis-for-a-delayed-sir-model-with-a-nonlinear-incidence-rateInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124Split equality problem for \(\kappa\)-asymptotically strictly pseudo-nonspreading mapping in Hilbert space58465852http://dx.doi.org/10.22436/jnsa.010.11.22ENYing ChenStatistical Research Institute, Naikai University, Tianjin, ChinaHaili GuoDepartment of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, ChinaLuoyi ShiDepartment of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, ChinaZhaojun WangStatistical Research Institute, Naikai University, Tianjin, ChinaIn this paper, we consider the split equality problem (SEP) in Hilbert space. We propose and investigate a new iterative
algorithm for solving split equality problem for \(\kappa\)-asymptotically strictly pseudo-nonspreading mapping. Finally, a numerical example is given to illustrate the feasibility of the proposed algorithm.http://www.isr-publications.com/jnsa/6186/download-split-equality-problem-for-kappa-asymptotically-strictly-pseudo-nonspreading-mapping-in-hilbert-spaceInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124Fixed point theorems for \(C\)-class functions in \(b\)-metric spaces and applications58535868http://dx.doi.org/10.22436/jnsa.010.11.23ENHuaping HuangSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, ChinaGuantie DengSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, ChinaStojan RadenovićFaculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, SerbiaThe aim of this paper is to present some fixed point results for \(C\)-class functions in the setting of \(b\)-metric spaces. Moreover, some examples are given to support the main results. In addition, by using our results, we obtain the existence and uniqueness of solution to differential or integral equation. Furthermore, for the differential equation, we provide the precise mathematical expression of solution.http://www.isr-publications.com/jnsa/6187/download-fixed-point-theorems-for-c-class-functions-in-b-metric-spaces-and-applicationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124Generalized harmonically convex functions on fractal sets and related Hermite-Hadamard type inequalities58695880http://dx.doi.org/10.22436/jnsa.010.11.24ENWenbing SunSchool of Science, Shaoyang University, Shaoyang 422000, Hunan, P. R. ChinaIn this paper, the author introduced the concept of generalized harmonically convex function on fractal sets \(\mathbb{R}^{\alpha}(0<\alpha\leq1)\) of real line numbers and established generalized Hermite-Hadamard's inequalities for generalized harmonically convex function. Then, by creating a local fractional integral identity, obtained some Hermite-Hadamard type inequalities of these classes of functions.http://www.isr-publications.com/jnsa/6188/download-generalized-harmonically-convex-functions-on-fractal-sets-and-related-hermite-hadamard-type-inequalitiesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124On the characterization of the solution set for vector equilibrium problem58815895http://dx.doi.org/10.22436/jnsa.010.11.25ENGang WangSchool of Management Science, Qufu Normal University, Shandong Rizhao, 276826, ChinaLijun GaoSchool of Engineering, Qufu Normal University, Shandong, Rizhao, 276826, ChinaIn this article, we investigate the nonemptiness and compactness
of the solution set for vector equilibrium problem defined in finite-dimensional spaces. We show that vector equilibrium problem has nonempty and compact solution set if and only if linearly scalarized equilibrium problem has nonempty and compact solution set provided that \(R_1=\{0\}\) holds. Furthermore, we obtain that vector equilibrium problem has nonempty and compact solution set if and only if linearly scalarized equilibrium problem has nonempty and compact solution set when coercivity condition holds. As applications, we employ the obtained results to derive Levitin-Polyak well-posedness, stability analysis and connectedness of the solution set of the vector equilibrium problem.http://www.isr-publications.com/jnsa/6189/download-on-the-characterization-of-the-solution-set-for-vector-equilibrium-problemInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124Infinitely many periodic solutions for second-order discrete Hamiltonian systems58965903http://dx.doi.org/10.22436/jnsa.010.11.26ENDa-Bin WangDepartment of Applied Mathematics, Lanzhou University of Technology, 730050 Lanzhou, People's Republic of ChinaQin XiaoDepartment of Applied Mathematics, Lanzhou University of Technology, 730050 Lanzhou, People's Republic of ChinaWen GuanDepartment of Applied Mathematics, Lanzhou University of Technology, 730050 Lanzhou, People's Republic of ChinaInfinitely many periodic solutions are obtained for a second-order discrete Hamiltonian systems by using the minimax methods in critical point theory. Our results extend and improve previously known results. http://www.isr-publications.com/jnsa/6191/download-infinitely-many-periodic-solutions-for-second-order-discrete-hamiltonian-systemsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124A modified infeasible homotopy algorithm for computing fixed point in general non-convex set59045913http://dx.doi.org/10.22436/jnsa.010.11.27ENZhichuan ZhuSchool of Statistics, Jilin University of Finance and Economics, Changchun, Jilin 130117, ChinaRuifeng WuSchool of Applied Mathematics, Jilin University of Finance and Economics, Changchun, Jilin 130117, ChinaYanchun XingSchool of Statistics, Jilin University of Finance and Economics, Changchun, Jilin 130117, ChinaIn this paper, to find a fixed point of self-mapping in the general
non-convex set with both equality constraints and inequality
constraints, a modified infeasible homotopy for perturbing only
inequality constraints is constructed and the global convergence of
the smooth homotopy pathways is proved under some much weaker
conditions. The advantage of the modified homotopy is that the
initial point needs to be only in the shifted set with only
inequality constraints, not necessarily, a feasible point in the
original set, and hence it is more convenient to be implemented than
the existing methods. The feasibility and effectiveness of the
modified homotopy method is shown by some numerical tests.http://www.isr-publications.com/jnsa/6192/download-a-modified-infeasible-homotopy-algorithm-for-computing-fixed-point-in-general-non-convex-setInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124On a functional equation connected with bi-linear mappings and its Hyers-Ulam stability59145921http://dx.doi.org/10.22436/jnsa.010.11.28ENKrzysztof CieplińskiFaculty of Applied Mathematics, AGH University of Science and Technology, Mickiewicza 30, 30-059 Krakow, PolandWe introduce the notion of a bi-linear mapping which generalizes some known ones, and note that bi-linear mappings satisfy a functional equation. The Hyers-Ulam stability of this equation is studied in Banach, \(2\)-Banach and complete non-Archimedean normed spaces.http://www.isr-publications.com/jnsa/6193/download-on-a-functional-equation-connected-with-bi-linear-mappings-and-its-hyers-ulam-stabilityInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124The split feasibility problems in an infinite dimensional space59225931http://dx.doi.org/10.22436/jnsa.010.11.29ENMingliang ZhangSchool of Mathematics and Statistics, Henan University, Kaifeng 475000, ChinaThe purpose of this article is to investigate the approximation of common solutions of fixed point and split feasibility problems. A viscosity iterative algorithm is introduced and studied for this approximation problem. Strong convergence theorems are established in an infinite dimensional real Hilbert space.http://www.isr-publications.com/jnsa/6194/download-the-split-feasibility-problems-in-an-infinite-dimensional-spaceInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124Strong convergence of Halpern method for firmly type nonexpansive mappings59325938http://dx.doi.org/10.22436/jnsa.010.11.30ENYonghong YaoInstitute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Sichuan 610054, ChinaMihai PostolacheChina Medical University, Taichung, Taiwan and University Politehnica of Bucharest, Bucharest, RomaniaNaseer ShahzadDepartment of Mathematics, King Abdulaziz University, P. O. B. 80203, Jeddah 21589, Saudi ArabiaIn this paper, Halpern method is applied to find fixed points of a
class of firmly type nonexpansive mappings. A strong convergence
result is obtained under the control conditions (C1) and (C2).
Our conclusion obtained in this paper gives the affirmative answer
of the Halpern open problem for this class of mapping.http://www.isr-publications.com/jnsa/6195/download-strong-convergence-of-halpern-method-for-firmly-type-nonexpansive-mappingsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124A fixed point theorem for systems of operator equations and its application59395946http://dx.doi.org/10.22436/jnsa.010.11.31ENYujun CuiState Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, P. R. ChinaA new fixed point theorem in product cones is established for systems of
operator equations, where the components are expressed by partial ordering. In applications, this allows the nonlinear term
of a differential system to have different behaviors in components.http://www.isr-publications.com/jnsa/6196/download-a-fixed-point-theorem-for-systems-of-operator-equations-and-its-applicationInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124Certain Ostrowski type inequalities for generalized \(s\)-convex functions59475957http://dx.doi.org/10.22436/jnsa.010.11.32ENMuharrem TomarDepartment of Mathematics, Faculty of Arts and Sciences, Ordu University, 52200 Ordu, TurkeyPraveen AgarwalDepartment of Mathematics, Anand International College of Engineering, Jaipur-303012, IndiaMohamed JleliDepartment of Mathematics, King Saud University, Riyadh-11451, Saudi ArabiaBessem SametDepartment of Mathematics, King Saud University, Riyadh-11451, Saudi ArabiaIn this paper, we first obtain a generalized integral identity for twice local
differentiable functions. Then, using functions whose second derivatives in absolute value
at certain powers are generalized \(s\)-convex in the second sense, we obtain some new Ostrowski type inequalities.http://www.isr-publications.com/jnsa/6197/download-certain-ostrowski-type-inequalities-for-generalized-s-convex-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124Expected residual minimization method for uncertain variational inequality problems59585975http://dx.doi.org/10.22436/jnsa.010.11.33ENCunlin LiSchool of Management, North Minzu University, Yinchuan, Ningxia 750021, ChinaZhifu JiaSchool of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia 750021, ChinaLin ZhangSchool of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia 750021, ChinaThis paper considers an uncertain variational inequality problem (UVIP).
We first establish UVIP as an optimization problem (ERM model) which minimizes
the expected residual of the so-called regularized gap function. Then, we make some assumptions about a
UVIP subclass in which the function involved is affine. Thus the priority in our paper is to discuss the properties of the ERM problem and comprehensive convergence analysis under uncertainty theory. In the end, we make a conclusion. http://www.isr-publications.com/jnsa/6198/download-expected-residual-minimization-method-for-uncertain-variational-inequality-problemsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124Dynamics analysis and numerical simulations of a new 5D Lorenz-type chaos dynamical system59765984http://dx.doi.org/10.22436/jnsa.010.11.34ENFuchen ZhangCollege of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, People's Republic of ChinaXiaofeng LiaoCollege of Electronic and Information Engineering, Southwest University, Chongqing 400715, People's Republic of ChinaChunlai MuCollege of Mathematics and Statistics, Chongqing University, Chongqing 401331, People's Republic of ChinaGuangyun ZhangCollege of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, People's Republic of ChinaXiaomin LiCollege of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, People's Republic of ChinaUltimate bound sets of chaotic systems have important applications in chaos control and chaos synchronization. Ultimate bound sets can also be applied in estimating the dimensions of chaotic attractors. However, it is often a difficult work to obtain the bounds of high-order chaotic systems due to complex algebraic structure of high-order chaotic systems. In this paper, a new 5D autonomous quadratic chaotic system which is different from the Lorenz chaotic system is proposed and analyzed. Ultimate bound sets and globally exponential attractive sets of this system are studied by introducing the Lyapunov-like functions. To validate the ultimate bound estimation, numerical simulations are also investigated.http://www.isr-publications.com/jnsa/6199/download-dynamics-analysis-and-numerical-simulations-of-a-new-5d-lorenz-type-chaos-dynamical-systemInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124Almost sure exponential stability for time-changed stochastic differential equations59855998http://dx.doi.org/10.22436/jnsa.010.11.35ENYongxiang ZhuCollege of Traffic Engineering, Hunan University of Technology, Zhuzhou, Hunan, 412007, ChinaMin ZhuCollege of Traffic Engineering, Hunan University of Technology, Zhuzhou, Hunan, 412007, ChinaJunping LiSchool of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, ChinaSome sufficient conditions for almost sure exponential stability of solutions to time-changed stochastic differential equations (SDEs) are presented.
The principle technique of our investigation is to construct a proper Lyapunov function and carry out generalized Lyapunov methods to time-changed SDEs. In contrast to the almost sure exponential stability in existing articles, we present new results on the stability of solutions to time-changed SDEs. Finally, an example is given to demonstrate the effectiveness of our work.http://www.isr-publications.com/jnsa/6200/download-almost-sure-exponential-stability-for-time-changed-stochastic-differential-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124On a completely non-unitary contraction and associated dissipative difference operator59996019http://dx.doi.org/10.22436/jnsa.010.11.36ENEkin UğurluCankaya University, Faculty of Arts and Science, Department of Mathematics, 06530 Balgat, Ankara, TurkeyDumitru BaleanuInstitute of Space Sciences, Magurele-Bucharest, RomaniaIn this paper, we investigate the spectral properties of dissipative
difference operator, dissipative sum operator and contractive
operator. Using Solomyak's method, we construct the characteristic
function of the dissipative difference operator. For this purpose,
we use boundary spaces and functional embeddings. Then we pass to
the characteristic function of the Cayley transform of the
dissipative difference operator which is a completely non-unitary
contraction belonging to the class \(C_{0}\). With the aid of this
characteristic function we achieve to pass to the minimal function
of the contraction and we investigate the complete spectral analysis
of both the contractive and dissipative operators. Embedding the
associated contraction to its natural unitary colligation, we obtain a Carathéodory function. Moreover, self-adjoint dilation of the maximal
dissipative difference operator and its incoming and outgoing
eigenfunctions are constructed. Finally, the truncated CMV matrix is
established which is unitary equivalent to the contractive operator.http://www.isr-publications.com/jnsa/6201/download-on-a-completely-non-unitary-contraction-and-associated-dissipative-difference-operatorInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171124Infinitely many solutions for a class of p-Laplacian equation with Sturm-Liouville type nonhomogeneous boundary conditions60206034http://dx.doi.org/10.22436/jnsa.010.11.37ENFenglong SunSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, PeopleLishan LiuSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, PeopleYonghong WuDepartment of Mathematics and Statistics, Curtin University, Perth, WA6845, AustraliaWe establish the criteria for the existence of infinitely many solutions for a class of one-dimensional p-Laplacian equations with Sturm-Liouville type nonhomogeneous boundary conditions. The nonlinear term has two parameters \(\lambda,\,\mu\) and is dependent on \(x\) and the derivative \(u'(x)\) of the solution to be determined. The main method used for the study is Ricceri's Variational Principle. http://www.isr-publications.com/jnsa/6202/download-infinitely-many-solutions-for-a-class-of-p-laplacian-equation-with-sturm-liouville-type-nonhomogeneous-boundary-conditionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171126Refinements of Hermite-Hadamard inequality for operator convex function60356041http://dx.doi.org/10.22436/jnsa.010.11.38ENJunmin HanSchool of Mathematics and Information Science, Weifang University, Weifang, 261061, P. R. ChinaJian ShiCollege of Mathematics and Information Science, Hebei University, Baoding, 071002, P. R. ChinaIn this paper, we present several operator versions of the Hermite-Hadamard inequality for the operator convex function, which are refinements of some operator convex inequalities presented by Dragomir [S. S. Dragomir, Appl. Math. Comput., \({\bf 218}\) (2011), 766--772] and [S. S. Dragomir, RGMIA Research Report Collection, \({\bf 2016}\) (2016), 15 pages].http://www.isr-publications.com/jnsa/6227/download-refinements-of-hermite-hadamard-inequality-for-operator-convex-functionInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171126Nontrivial solutions for a fractional differential equation with nonlocal Riemann-Stieltjes boundary conditions60426055http://dx.doi.org/10.22436/jnsa.010.11.39ENXinguang ZhangSchool of Mathematical and Informational Sciences,Yantai University,Yantai 264005, Shandong, ChinaLishan LiuSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, ChinaYonghong WuDepartment of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, AustraliaYujun CuiDepartment of Mathematics, Shandong University of Science and Technology, Qingdao, 266590, Shandong, ChinaThe model of fractional differential equation arises from various fields of physics, engineering, and applied mathematics. In this paper,
we focus on the existence and uniqueness of nontrivial solutions for a abstract model of fractional differential equation with nonlocal Riemann-Stieltjes boundary conditions. Under certain suitable growth conditions, we establish some sufficient conditions for the existence and uniqueness of nontrivial solutions based on Leray-Schauder nonlinear alternative and Schauder fixed point theorem.http://www.isr-publications.com/jnsa/6228/download-nontrivial-solutions-for-a-fractional-differential-equation-with-nonlocal-riemann-stieltjes-boundary-conditionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171127Existence and multiplicity of positive solutions for a nonlocal problem60566061http://dx.doi.org/10.22436/jnsa.010.11.40ENYu DuanCollege of Science, Guizhou University of Engineering Science, Bijie Guizhou 551700, People's Republic of ChinaXin SunCollege of Science, Guizhou University of Engineering Science, Bijie Guizhou 551700, People's Republic of ChinaHong-Ying LiSchool of Mathematics and Information, China West Normal University, Nanchon, Sichuan 637002, People's Republic of China In this work, we are interested in considering the following nonlocal problem
\[
\begin{cases}
-\left(a-b\displaystyle\int_{\Omega}|\nabla u|^2dx\right)\Delta u= f(x)|u|^{p-2}u,
\quad\text{in }\Omega, \\
u=0, \quad\text{on }\partial\Omega,
\end{cases}
\]
where \(\Omega\subset\mathbb{R}^{N}~(N\geq3)\) is a bounded domain with smooth boundary \(\partial\Omega, a,b>0, 1\leq p<2^*\),
\(f\in L^{\frac{2^*}{2^{*}-p}}(\Omega)\) is nonzero and nonnegative. By using the variational method, some existence and multiplicity results are obtained.http://www.isr-publications.com/jnsa/6229/download-existence-and-multiplicity-of-positive-solutions-for-a-nonlocal-problemInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171127Topological conjugacy of PM functions with height equaling \(\infty\)60626070http://dx.doi.org/10.22436/jnsa.010.11.41ENPingping ZhangDepartment of Mathematics, Binzhou University, Shandong 256603, P. R. ChinaIt is known that topological conjugacy
is a basic equivalence relation in
dynamical systems.
In this paper we study a class of piecewise monotone and continuous functions
with infinite height. Those
functions are topologically conjugate with each other if and only if
they have same sequences describing itineraries of all forts, endpoints, and fixed points.
We construct the topological conjugacy by extension, which partly generalizes previous results. http://www.isr-publications.com/jnsa/6230/download-topological-conjugacy-of-pm-functions-with-height-equaling-inftyInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171127Analysis of a delayed SIR model subject to multiple infectious stages and nonlinear incidence rate60716083http://dx.doi.org/10.22436/jnsa.010.11.42ENHong ZhangSchool of Mathematical Science, Harbin Normal University, Harbin 150025, ChinaChunming LiSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaHongquan SunSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaWe investigate the threshold dynamics problem of a delayed Susceptible-Infected-Recovered (SIR) model with general nonlinear incidence and multiple parallel infectious stages. Biologically, the model contains the following aspects:
(i) once infection occurs, a fraction of the infected individuals is detected and treated, while the rest of the infected remains undetected and untreated;
(ii) distributed delays governed by a general nonlinear incidence function are included into the model due to the complexity of disease transmissions.
Mathematically, under some suitable assumptions on nonlinear incidence rate, we prove that the reproduction number \(\Re_0 \) can be used to govern the the global dynamics of the model. The proofs of global attractivity of disease-free equilibrium (which means the extinction of disease) and endemic equilibrium (which means the persistence of the disease) are achieved by constructing suitable Lyapunov functionals.http://www.isr-publications.com/jnsa/6231/download-analysis-of-a-delayed-sir-model-subject-to-multiple-infectious-stages-and-nonlinear-incidence-rateInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171130Fixed points for multivalued contractions with respect to a Pompeiu type metric60846101http://dx.doi.org/10.22436/jnsa.010.11.43ENIulia CoroianDepartment of Land Measurements and Exact Sciences, University Of Agricultural Sciences and Veterinary Medicine, 3-5 Manastur St., 400372 Cluj-Napoca, RomaniaThe purpose of this paper is to present a fixed point theory for multivalued \(H^+\)-contractions from
the following perspectives: existence/uniqueness of the fixed and strict fixed points, data dependence of the fixed point set,
sequence of multivalued operators and fixed points, Ulam-Hyers stability of a multivalued fixed point equation, well-posedness of the fixed point problem, limit shadowing property for a multivalued operator, set-to-set operatorial equations and fractal operator theory.http://www.isr-publications.com/jnsa/6283/download-fixed-points-for-multivalued-contractions-with-respect-to-a-pompeiu-type-metricInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171130A mass-conservative characteristic splitting mixed element method for saltwater intrusion problem61026118http://dx.doi.org/10.22436/jnsa.010.11.44ENJiansong ZhangDepartment of Applied Mathematics, China University of Petroleum, Qingdao 266580, ChinaYuezhi ZhangDepartment of Applied Mathematics, China University of Petroleum, Qingdao 266580, ChinaZhaohui LiuDepartment of Applied Mathematics, China University of Petroleum, Qingdao 266580, ChinaA new characteristic mixed finite element method is developed for solving saltwater intrusion problem. In this algorithm, the splitting mixed finite element (SMFE) method is applied for solving the parabolic-type water head equation, and the mass-conservative characteristic (MCC) finite element method is applied for solving the convection-diffusion type concentration equation. The application of the splitting mixed element method results in a symmetric positive definite coefficient matrix of the mixed element system and separating the flux equation from the water head equation. While the mass-conservative characteristic finite element method does well in handling convection-dominant diffusion problem and keeps mass balance. The convergence of this method is considered and the optimal \(L^2\)-norm error estimate is also derived.http://www.isr-publications.com/jnsa/6284/download-a-mass-conservative-characteristic-splitting-mixed-element-method-for-saltwater-intrusion-problemInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171130Anti-periodic solutions for neutral type FCNNs with time-varying delays and \(D\) operator on time scales61196131http://dx.doi.org/10.22436/jnsa.010.11.45ENBing LiSchool of Mathematics and Computer Science, Yunnan Nationalities University, Kunming, Yunnan 650500, People's Republic of ChinaYongkun LiDepartment of Mathematics, Yunnan University, Kunming, Yunnan 650091, People's Republic of ChinaIn this paper, we consider a class of neutral type fuzzy cellular neural networks with time-varying delays and \(D\) operator on time scales. Based on inequality analysis techniques on time scales and a fixed point theorem and the theory of calculus on time scales, we obtain the existence and global exponential stability of anti-periodic solutions for this class of the networks. Finally, a numerical example is given to illustrate the feasibility of our results.http://www.isr-publications.com/jnsa/6285/download-anti-periodic-solutions-for-neutral-type-fcnns-with-time-varying-delays-and-d-operator-on-time-scalesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101120171130Dynamics of Lotka-Volterra diffusion-advection competition system with heterogeneity vs homogeneity61326140http://dx.doi.org/10.22436/jnsa.010.11.46ENBenlong XuDepartment of Mathematics, Shanghai Normal University, Shanghai, 200234, P. R. ChinaHongyan JiangDepartment of Mathematics, Shanghai Normal University, Shanghai, 200234, P. R. China This paper mainly studies the dynamics of a Lotka-Volterra reaction-diffusion-advection model for two competing species which disperse by both random diffusion and advection along environmental gradient. In this model, the species are assumed to be identical except spatial variation: one lives in the heterogeneity environment, the other lives in the homogeneity environment. The main results of this paper are two fold: (i) The species living in homogeneous environment can never wipe out their competitor; (ii) Explore the condition on the diffusion and advection rates for exclusion and coexistence.
It is proved that for fixed dispersal rates, when the strength of the advection is sufficiently strong, the two competitive species coexist. This is a remarkable different result with that obtained by He and Ni recently for
corresponding systems without advection [X. He, W.-M. Ni, J. Differential Equations, \({\bf254}\) (2013), 528--546].http://www.isr-publications.com/jnsa/6286/download-dynamics-of-lotka-volterra-diffusion-advection-competition-system-with-heterogeneity-vs-homogeneity