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2008
1
2
ISSN 2008-1898
66
SOME REMARK ON THE NONEXISTENCE OF POSITIVE SOLUTIONS FOR SOME alpha, P-LAPLACIAN SYSTEMS
SOME REMARK ON THE NONEXISTENCE OF POSITIVE SOLUTIONS FOR SOME alpha, P-LAPLACIAN SYSTEMS
en
en
This paper deals with nonexistence result for positive solution in
\(C^1(\overline{\Omega})\) to the following reaction-diffusion system
\[
\begin{cases}
-\Delta_{a,p}u = a_1v^{p-1} - b_1v^{\gamma -1} - c,\,\,& \,\,x\in \Omega,\\
-\Delta_{a,p}v = a_1u^{p-1} - b_1u^{\gamma -1} - c,\,\,& \,\,x\in \Omega, \qquad (0.1)\\
u = 0 = v \,\,& \,\,x\in \partial \Omega,
\end{cases}
\]
where \(\Delta_{a,p}\) denotes the \(a, p\)-Laplacian operator defined by \(\Delta_{a,p}z=div(a| \nabla z|^{p-2}\nabla z); p>1, \gamma(>p); a_1, b_1 \) and \(c\) are positive constant, \(\Omega\) is a smooth
bounded domain in \(\mathbb{R}^N(N \geq1)\) with smooth boundary and \(a(x) \in L^\infty(\Omega),
a(x) \geq a_0 > 0\) for all \(x\in\Omega\) .
56
60
M.
ALIMOHAMMADY
Islamic Azad University, branch Noor, Iran
M.
KOOZEGAR
Department of Mathematics, University of Mazandaran, Babolsar 47416 - 1468, Iran.
p
a-Laplacian
nonexistence
positive solution
reaction-diffusion systems.
Article.1.pdf
[
[1]
G. A. Afrouzi, S. H. Rasouli , A remark on the nonexistence of positive solutions for some p-Laplacian systems , Global J. Pure. Appl. Math., 1/2 (2005), 197-201
##[2]
G. A. Afrouzi, S. H. Rasouli, Population models involving the p-Laplacian with indefinite weight and constant yeild harvesting. , chaos, Solutions and Fractals, , 31 (2007), 404-408
##[3]
L. Boccardo , D. G. Figueiredo, Some remarks on a system of quasilinear elliptic equations, Nonl. Diff. Eqns. Appl., 9 (2002), 231-240
##[4]
P. Clement, J. Fleckinger, E. Mitidieri , F. de Thelin, Existence of positive solutions for a nonvariational quasilinear elliptic system, J. Diff. Eqns. , 166 (2000), 455-477
##[5]
R. Dalmasso, Existence and uniqueness of positive solutions of a semilinear elliptic system, Nonl. Anal. , 39 (2000), 559-568
##[6]
A. Djellit, S. Tas, On some nonlinear elliptic systems, Nonl. Anal., 59 (2004), 675-706
##[7]
D. D. Hai , On a cllas of sublinear quasilinear elliptic problems, Proc. Amer. Math. Soc., 131 (2003), 2409-2414
##[8]
S. Oruganti , J. Shi, R. Shivaji , Logistic equation with the p-Laplacian and constant yeild harvesting, Applied. Anal., 9 (2004), 723-727
]
AN IMPLICIT METHOD FOR FUZZY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
AN IMPLICIT METHOD FOR FUZZY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
en
en
In this paper, we consider an implicit finite difference method for
solving fuzzy partial differential equations (FPDEs). We present stability of
this method and solve the parabolic equation with this scheme.
61
71
K.
NEMATI
Islamic Azad University, Nur branch, Nur, Iran.
M.
MATINFAR
Department of Mathematics, University of Mazandaran, Babolsar, Iran.
Parabolic boundary value problems
Fuzzy partial difference method
Implicit method.
Article.2.pdf
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[1]
T. Allahviranloo , Difference methods for fuzzy partial differential equations , Computational Methods in Applied Mathematics, 2 (3) (2002), 233-242
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T. Allahviranloo, M. Afshar , Difference method for solving the fuzzy parabolic equations, Applied Mathematical Sciences, 1 (27) (2007), 1299-1309
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T. Allahviranloo, N. Ahmadi, E. Ahmadi, Kh. Shams Alketabi , Block Jacobi two-stage method for fuzzy systems of linear equations, Applied Mathematics and Computation , 175 (2006), 1217-1228
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]
IMPULSIVE STABILIZATION OF CELLULAR NEURAL NETWORKS WITH TIME DELAY VIA LYAPUNOV FUNCTIONALS
IMPULSIVE STABILIZATION OF CELLULAR NEURAL NETWORKS WITH TIME DELAY VIA LYAPUNOV FUNCTIONALS
en
en
This paper investigates the problem of global exponential stability
for a class of impulsive cellular neural networks with time delay. By employing
Lyapunov functionals, some sufficient conditions for exponential stability are
established. Our results show that unstable cellular neural networks with time
delay may be stabilized by impulses, where the upper bound of the amplitudes
of the impulses is given. Numerical simulations on two examples are given to
illustrate our results.
72
86
QING
WANG
Department of Computer Science, Mathematics, and Engineering, Shepherd University, Shepherdstown, WV 25443,USA
XINZHI
LIU
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1
Impulsive cellular neural networks
global exponential stability
stabilization
time delay
Article.3.pdf
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[1]
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S. Arik, V. Tavsanglu, On the global asymptotic stability of delayed cellular neural networks, IEEE Trans. Circuits Syst. I, 47 (2000), 571-574
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K. Gopalsamy , Stability of artificial neural networks with impulses, Applied Mathematics and Computation, 154 (2004), 783-813
##[11]
X. Li, L. Huang, J. Wu, Further results on the stability of delayed cellular neural networks, IEEE Trans. Circuits Syst. I, 50 (2003), 1239-1242
##[12]
X. Liu, Q. Wang , Exponential Stability of Impulsive Functional Differential Equations via Lyapunov Functionals, Nonlinear Analysis, (to appear)
##[13]
L. Rong, LMI approach for global periodicity of neural networks with time-varying delays, IEEE Trans. Circuits Syst. I, 52 (2005), 1451-1458
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T. Roska, C. Wu, M. Balsi, L. Chua , Stability and dynamics of delay-type general and cellular neural networks, IEEE Trans. Circuits Syst., 39 (1992), 487-490
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T. Roska, C. Wu, L. Chua , Stability of Cellular Neural Networks with Dominant Nonlinear and Delay-Type Template, IEEE Trans Circuits Syst. I, 40 (1993), 270-272
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N. Takahshi , A new suffcient condition for complete stability of cellular neural networks with delay, IEEE Trans. Circuits Syst. I, 47 (2000), 793-799
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Q. Wang, X. Liu , Exponential stability for impulsive delay differential equations by Razumikhin method, J. Math. Anal. Appl., 309 (2005), 462-473
##[19]
Q. Wang, X. Liu , Global Exponential Stability of Impulsive High Order Hopfield Type Neural Networks with Delays, Proceeding of the DSDIC 4th International Conference on Engineering Applications and Computational Algorithms, Watam Press, 825-830. (2005)
##[20]
B. Xu, X. Liu, X. Liao , Global asymptotic stability of high-order Hopfield type neural networks with time delays, Computers and Mathematics with Applications, 45 (2003), 1729-1737
##[21]
D. Xu, Z. Yang, Impulsive delay differential inequality and stability of neural networks, J. Math. Anal. Appl., 305 (2005), 107-120
]
A NOTE ON \(D_{11}\)-MODULES
A NOTE ON \(D_{11}\)-MODULES
en
en
Let \(M\) be a right R-module. \(M\) is called \(D_{11}\)-module if every
submodule of \(M\) has a supplement which is a direct summand of \(M\) and \(M\)
is called a \(D^+_{11}\)- module if every direct summand of \(M\) is a \(D_{11}\)- module. In
this paper we study some properties of \(D_{11}\) modules.
87
90
Y.
TALEBI
Department of Mathematics, University of Mazandaran, Babolsar, Iran.
M.
VEYLAKI
Department of Mathematics, University of Mazandaran, Babolsar, Iran.
\(D_{11}\)- module
\(D^+_{11}\)- module
Article.4.pdf
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[1]
F. W. Anderson, K. R. Fuller, Rings and categories of modules, Berlin, Springer- verlag, New York (1992)
##[2]
G. F. Birkenmeier, A. Tercan , When some complement of a submodule is a summand , Comm. Algebra , 35 (2007), 597-611
##[3]
A. Ozcan, Harmanic Duo modules , Glasgow Math. J., 48(3) (2006), 535-545
##[4]
Y. Talebi, N. Vanaja, The Torsion theory cogenerated by M-small modules, Comm.Algebra , 30(3) (2002), 1449-1460
##[5]
Y. Wang , A Note on modules with (\(D^+_{ 11}\)), Southeast Asian Bulletin of Mathematics , 28 (2004), 999-1002
##[6]
R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia (1991)
]
BLOW-UP TIME OF SOME NONLINEAR WAVE EQUATIONS
BLOW-UP TIME OF SOME NONLINEAR WAVE EQUATIONS
en
en
In this paper, we consider the following initial-boundary value
problem
\[
\begin{cases}
u_{tt}(x, t) = \varepsilon Lu(x, t) + b(t)f(u(x, t)) ,\,\,\,\,\, \texttt{in} \qquad\Omega\times (0, T),\\
u(x, t) = 0 ,\,\,\,\,\, \texttt{on} \qquad\partial\Omega\times (0, T),\\
u(x, 0) = 0 ,\,\,\,\,\, \texttt{in}\qquad \Omega,\\
u_t(x, 0) = 0 ,\,\,\,\,\, \texttt{in}\qquad \Omega,
\end{cases}
\]
where \(\varepsilon\) is a positive parameter, \(b \in C^1(\mathbb{R}_+), b(t) > 0, b' (t)\geq 0, t \in \mathbb{R}_+, f(s) \)
is a positive, increasing and convex function for nonnegative values of s. Under
some assumptions, we show that, if \(\varepsilon\) is small enough, then the solution u of
the above problem blows up in a finite time, and its blow-up time tends to that
of the solution of the following differential equation
\[
\begin{cases}
\alpha' (t) = b(t)f(\alpha(t)),\quad t > 0,\\
\alpha(0) = 0, \alpha'(0) = 0.
\end{cases}
\]
Finally, we give some numerical results to illustrate our analysis.
91
101
THEODORE K.
BONI
Institut National Polytechnique Houphouet-Boigny de Yamoussoukro, BP 1093 Yamoussoukro, (Cote d'Ivoire).
DIABATE
NABONGO
Universite d'Abobo-Adjame, UFR-SFA, Departement de Mathematiques et Informatiques, 16 BP 372 Abidjan 16, (Cote d'Ivoire)
ROGER B.
SERY
Institut National Polytechnique Houphouet-Boigny de Yamoussoukro, BP 1093 Yamoussoukro, (Cote d'Ivoire).
Nonlinear wave equation
blow-up
convergence
numerical blow-up time.
Article.5.pdf
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]
STUDY OF A PREY-PREDATOR DYNAMICS UNDER THE SIMULTANEOUS EFFECT OF TOXICANT AND DISEASE
STUDY OF A PREY-PREDATOR DYNAMICS UNDER THE SIMULTANEOUS EFFECT OF TOXICANT AND DISEASE
en
en
A mathematical model is proposed to study the simultaneous effects of toxicant and infectious disease on Lotka-Volterra prey-redator system.
It is considered in the model that only the prey population is being affected by
disease and toxicant both, and the susceptible and infected prey populations
are being predated by predator. All the feasible equilibrium of the model are
obtained and the condition for the existence of interior equilibrium point is also
been determined. The criteria for both local stability and instability involving ecotoxicological and epidemiological parameters are derived. The global
stability of the interior equilibrium point is discussed using Lyapunov's direct
method. The results are compared with the case when environmental toxicant
is absent. Moreover, threshold conditions depending upon toxicant, disease
and predation related parameters for the non-linear stability of the model is
determined. Finally, the numerical verifications of analytic results are carried
out.
102
117
SUDIPA
SINHA
School of Mathematics and Allied Sciences, Jiwaji University Gwalior (M.P.)- 474011, INDIA.
O.P.
MISRA
School of Mathematics and Allied Sciences, Jiwaji University Gwalior (M.P.)- 474011, INDIA.
JOYDIP
DHAR
Department of Applied Sciences, ABV-Indian Institute of Information Technology and management, Gwalior(M.P.)-474011, INDIA.
Prey-Predator Dynamics
Disease
Toxicant
Stability
Simulation.
Article.6.pdf
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B. Liu, L. Chen, Y. Zhang, The effect of impulsive toxicant input on a population in a polluted environment, Journ. of biol.Sys. , 11(3) (2003), 265-274
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D. Mukherjee, Persistence and global stability of a population in a polluted environment with delay, J. Biol. Sys., 10 (2002), 225-232
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]
WHEN IS A QUASI-P-PROJECTIVE MODULE DISCRETE
WHEN IS A QUASI-P-PROJECTIVE MODULE DISCRETE
en
en
It is well-known that every quasi-projective module has \(D_2\)-condition.
In this note it is shown that for a quasi-p-projective module M which is self-
generator, duo, then M is discrete.
118
120
Y.
TALEBI
Department of Mathematics, University of Mazandaran, Babolsar, Iran.
I. KHALILI
GORJI
Supplemented Module
H-Supplemented Module
Lifting Module.
Article.7.pdf
[
[1]
G. F. Birkenmeier, B. J. Muller, S. T. Rizvi, Modules in which Every Fully Invariant submodule is Essential in a Fully Invariant Direct Summand, Comm. Algebra, 30 (2002), 1833-1852
##[2]
S. Chotchaisthit, When is a Quasi-p-injective Module Continuous? , Southest Asian Bulletin of Mathematics , 26 (2002), 391-394
##[3]
S. M. Mohamed, B. J. Muller, Continuous and Discrete Modules, London Math, Soc, Lecture Notes Series 147, University Press, Cambridge (1990)
##[4]
R. Wisbauer, Foundations of Module and Ring Theory , Gordon and Breach, Philadelphia (1991)
]
A COUNTEREXAMPLE TO COMMON FIXED POINT THEOREM IN PROBABILISTIC QUASI-METRIC SPACE
A COUNTEREXAMPLE TO COMMON FIXED POINT THEOREM IN PROBABILISTIC QUASI-METRIC SPACE
en
en
We give a counterexample to the paper ''Common fixed point
theorem in probabilistic quasi-metric space'' published in the first issue of this
journal.
121
122
DOREL
MIHET
West University of Timişoara, Faculty of Mathematics and Computer Science; Bv. V. Parvan 4, 300223 Timişoara, Romania
Probabilistic metric spaces
quasi-metric spaces
fixed point theorem
R-weakly commuting maps
triangle function.
Article.8.pdf
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[1]
M. Grabiec, Y. J. Cho, V. Radu, On nonsymmetric topological and probabilistic structures, Nova Publishers ., (2006)
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Gerald Jungck , Commuting Mappings and Fixed Points, The American Mathematical Monthly, 83(4) (1976), 261-263
##[3]
A. R. Shabani, S. Ghasempour, Common fixed point theorem in probabilistic quasi-metric space, J. Nonlinear Sci. Appl. , 1(1) (2008), 31-35
##[4]
R. Vasuki, P. Veeramani, Fixed point theorems and Cauchy sequences in fuzzy metric spaces, Fuzzy Sets and Systems, 135 (3) (2003), 415-417
]