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$$d_2$$-coloring of a Graph $$d_2$$-coloring of a Graph en en A subset S of V is called an i-set ($$i\geq 2$$) if no two vertices in S have the distance i. The 2-set number $$\alpha_2(G)$$ of a graph is the maximum cardinality among all 2-sets of G. A $$d_2$$-coloring of a graph is an assign- ment of colors to its vertices so that no two vertices have the distance two get the same color. The $$d_2$$-chromatic number $$\chi_{d_2}(G)$$ of a graph G is the minimum number of $$d_2$$-colors need to G. In this paper, we initiate a study of these two new parameters. 102 111 K. Selvakumar S. Nithya $$d_2$$-coloring $$d_2$$-chromatic number Article.1.pdf  G. Chartrand, L. Lesniak, Graphs and Digraphs, Wadsworth and Brooks/Cole, Monterey (1986) ## G. Fertin, E. Godard, A. Raspaud, Acyclic and k-distance coloring of the Grid, Information Processing Letters, 87 (2003), 51-58 ## J. Van den Heuvel, S. McGuinness, Colouring the square of a planar graph, J. Graph Theory, 42 (2005), 110-124
Nonexistence of Result for some p-Laplacian Systems Nonexistence of Result for some p-Laplacian Systems en en We study the nonexistence of positive solutions for the system $\begin{cases} -\Delta_{p}u=\lambda f(v),\,\,\,\,\, x\in \Omega,\\ -\Delta_{p}v=\mu g(u),\,\,\,\,\, x\in \Omega,\\ u=0=v,\,\,\,\,\, x\in \partial \Omega. \end{cases}$ where $$\Delta_p$$ denotes the p-Laplacian operator defined by $$\Delta_pz=div(|\nabla z|^{p-2} \nabla z)$$ for $$p >1$$ and $$\Omega$$ is a smooth bounded domain in $$N^R (N \geq 1)$$ , with smooth boundary $$\partial \Omega$$ , and $$\lambda$$ , $${\mu}$$ are positive parameters. Let $$f,g: [0,\infty)\rightarrow R$$ be continuous and we assume that there exist positive numbers $$K_i$$ and $$M_i ; i = 1;2$$ such that $$f(v)\leq k_1v^{p-1}-M_1$$ for all $$v\geq 0$$ ; and $$g(u)\leq k_2u^{p-1}-M_2$$ for all $$u\geq 0$$; We establish the nonexistence of positive solutions when $$\lambda_{\mu}$$ is large. 112 116 G. A. Afrouzi Z. Valinejad positive solutions p-Laplacian operator smooth bounded domain Article.2.pdf  G. A. Afrouzi, S. H. Rasouli, Population models involving the p-Laplacian with indefinite weight and constant yeild harvesting , Chaos Solitons Fractals, Vol. 31, 404--408 (2007) ## L. Boccardo, D. G. Figueiredo, Some remarks on a system of quasilinear elliptic equations, Nonl. Diff. Eqns. Appl., 9 (2002), 231-240 ## P. Clement, J. Fleckinger, E. Mitidieri, F. de Thelin, Existence of positive solutions for a nonvariational quasilinear elliptic systems, Journal of Differential Equations, 166 (2000), 455-477 ## R. Dalmasso, Existence and uniqueness of positive solutions of semilinear elliptic systems, Nonlinear Anal., 39 (2000), 559-568 ## A. Djellit, S. Tas, On some nonlinear elliptic systems, Nonlinear Anal., 59 (2004), 695-706 ## D. D. Hai, On a class of sublinear quasilinear elliptic problems, Proc. Amer. Math. Soc., 131 (2003), 2409-2414 ## G. A. Afrouzi, S. H. Rasouli, A remark on the Nonexistence of positive solutions for some p-Laplacian Systems., Global J. Pure. Appl. Math., 2005 (2005), 197-201
Multiple Solutions for a Two-point Boundary Value Problem Depending on Two Parameters Multiple Solutions for a Two-point Boundary Value Problem Depending on Two Parameters en en In this paper we deal with the existence of at least three weak solutions for a two-point boundary value problem with Neumann boundary condition. The approach is based on variational methods and critical point theory. 117 125 Shapour Heidarkhani Javad Vahidi Three solutions Critical point Multiplicity results Neumann problem. Article.3.pdf  G. A. Afrouzi, S. Heidarkhani, Three solutions for a Dirichlet boundary value problem involving the p-Laplacian, Nonlinear Anal., 66 (2007), 2281-2288 ## D. Averna, G. Bonanno, Three solutions for a Neumann boundary value problem involving the p-Laplacian, Le Matematiche, 60 (2005), 81-91 ## R. I. Avery, J. Henderson, Three symmetric positive solutions for a second-order boundary value problem, Appl. Math. Lett., 13 (2000), 1-7 ## G. Bonanno, Existence of three solutions for a two point boundary value problem, Appl. Math. Lett., 13 (2000), 53-57 ## G. Bonanno, Multiple solutions for a Neumann boundary value problem, J. Nonlinear Convex Anal., 4 (2003), 287-290 ## G. Bonanno, P. Candito, Three solutions to a Neumann problem for elliptic equations involving the p-Laplacian, Arch. Math., 80 (2003), 424-429 ## A. R. Miciano, R. Shivaji, Multiple positive solutions for a class of semipositone Neumann two point boundary value problems, J. Math. Anal. Appl., 178 (1993), 102-115 ## M. Ramaswamy, R. Shivaji, Multiple positive solutions for classes of p-Laplacian equations, Differential and Integral Equations, 17 (2004), 1255-1261 ## B. Ricceri, A three critical points theorem revisited, Nonlinear Anal., 70 (2009), 3084-3089 ## B. Ricceri, Existence of three solutions for a class of elliptic eigenvalue problem, Math. Comput. Modelling, 32 (2000), 1485-1494 ## B. Ricceri, On a three critical points theorem, Arch. Math., 75 (2000), 220-226
A Remark on Positive Solution for a Class of p,q-Laplacian Nonlinear System with Sign-changing Weight and Combined Nonlinear Effects A Remark on Positive Solution for a Class of p,q-Laplacian Nonlinear System with Sign-changing Weight and Combined Nonlinear Effects en en In this article, we study the existence of positive solution for a class of (p; q)- Laplacian system $\begin{cases} -\Delta_{p}u=\lambda a(x)f(u)h(v),\,\,\,\,\, x\in \Omega,\\ -\Delta_{p}v=\lambda b(x)g(u)k(v),\,\,\,\,\, x\in \Omega,\\ u=v=0,\,\,\,\,\, x\in \partial \Omega. \end{cases}$ where $$\Delta_p$$ denotes the p-Laplacian operator defined by $$\Delta_pz=div(|\nabla z|^{p-2} \nabla z), p>1,\Omega>0$$ is a parameter and $$\Omega$$ is a bounded domain in $$R^N(N > 1)$$ with smooth boundary $$\partial \Omega$$. Here $$a(x)$$ and $$b(x)$$ are $$C^1$$ sign-changing functions that maybe negative near the boundary and $$f, g, k, h$$ are $$C^1$$ nondecreasing functions such that $$f; g; h; k : [0,\infty)\rightarrow [0,\infty) ; f(s), k(s), h(s), g(s) > 0 ; s > 0$$ and $\lim_{x\rightarrow \infty}\frac{h(A(g(x))^{\frac{1}{q-1}})(f(x))^{p-1}}{x^{p-1}}=0$ for every $$A > 0$$. We discuss the existence of positive solution when $$h, k, f, g, a(x)$$ and $$b(x)$$ satisfy certain additional conditions. We use the method of sub-super solutions to establish our results. 126 134 S. H. Rasouli Z. Halimi Z. Mashhadban (p،q)- Laplacian system Sign-changing weight. Article.4.pdf  C. Atkinson, K. El-Ali, Some boundary value problems for the Bingham model, J. Non-Newtonian Fluid Mech., 41 (1992), 339-363 ## J. F. Escobar, Uniqueness theorems on conformal deformations of metrics, Sobolev inequalities, and an eigenvalue estimate, Comm. Pure Appl. Math., 43 (1990), 857-883 ## P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations, 51 (1984), 126-150 ## G. S. Ladde, V. Lakshmikantham, A. S. Vatsale, Existence of coupled quase-solutions of systems of nonlinear elliptic boundary value problems, Nonlinear Anal., 8 (1984), 501-515 ## N. Dancer, Competing species systems with diffusion and large interaction, Rendiconti del Seminario Matematico e Fisico di Milano (Milan Journal of Mathematics), 65 (1995), 23-33 ## J. Ali, R. Shivaji, An existence result for a semipositone problem with a sign-changing weight, Abstr. Appl. Anal., 2006 (2006), 1-5 ## M. Chhetri, S. oruganti, R. Shivaji, Existence results for a class of p-Laplacian problems with sign-changing weiht, Diff. Int. Equs., 18 (2005), 991-996 ## R. Dalmasso, Existence and uniqueness of positive solutions of semilinear elliptic systems, Nonlinear Analysis: Theory, Methods & Applications, 39 (2000), 559-568 ## J. Ali, R. Shivaji, M. Ramaswamy, Multiple positive solutions for a class of elliptic systems with combined nonlinear effects, Differential and Integral Equations, 19 (2006), 669-680 ## D. D. Hai, R. Shivaji, An existence result on positive solutions for a class of semilinear elliptic systems, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 134 (2004), 137-141 ## D. D. Hai, R. Shivaji, An existence result on positive solutions for a class of p-Laplacian systems, Nonlinear Analysis: Theory, Methods & Applications, 56 (2004), 1007-1010 ## A. Canada, P. Drabek, J. L. Gamez, Existence of positive solutions for some problems with nonlinear diffusion, Trans. Amer. Math. Soc., 349 (1997), 4231-4249 ## P. Drabek, J. Hernandez, Existence and uniqueness of positive solutions for some quasilinear elliptic problem, Nonlinear Anal., 44 (2001), 189-204 ## A. Ambrosetti, J. G. Azorero, I. Peral, Existence and multiplicity results for some nonlinear elliptic equations: a survey, Rend. Mat. Appl., 20 (2000), 167-198 ## C. O. Alves, D. G. De Figueiredo, Nonvariational elliptic systems, Discr. Contin. Dyn. Systems-A, 8 (2002), 289-302 ## G. A. Afrouzi, S. H. Rasouli, A remark on the existence of multiple solutions to a multiparameter nonlinear elliptic system, Nonlinear Analysis: Theory, Methods & Applications, 71 (2009), 445-455 ## G. A. Afrouzi, S. H. Rasouli, A remark on the linearized stability of positive solutions for systems involving the p-Laplacian, Positivity, 11 (2007), 351-356 ## A. Djellit, S. Tas, On some nonlinear elliptic systems, Nonlinear Analysis: Theory, Methods & Applications, 59 (2004), 695-706 ## D. D. Hai, Uniqueness of positive solutions for a class of semilinear elliptic systems, Nonlinear Analysis: Theory, Methods & Applications, 52 (2003), 596-603
A New Analytical Approach to Solve Exponential Stretching Sheet Problem in Fluid Mechanics by Variational Iterative Pade Method A New Analytical Approach to Solve Exponential Stretching Sheet Problem in Fluid Mechanics by Variational Iterative Pade Method en en In this article, we present a reliable combination of variational iterative method and Padé approximants to investigate two dimensional exponential stretching sheet problem. The proposed method is called variational iterative Pade´ method (VIPM). The method is capable of reducing the size of calculation and easily overcomes the difficulty of perturbation methods or Adomian polynomials. The results reveal that the VIPM is very effective and is easy to apply. 135 144 Majid Khan Muhammad Asif Gondal Sunil Kumar Variational iterative method Pade´ approximation Exponential stretching sheet Similarity transforms Series solution. Article.5.pdf  G. Adomian, Solving frontier problems of physics: the decomposition method, Springer, Dordrecht (1994) ## M. M. Hosseini, Adomian decomposition method with Chebyshev polynomials, Appl. Math. Comput., 175 (2006), 1685-1693 ## M. M. Hosseini, Numerical solution of ordinary differential equations with impulse solution, Appl. Math. Comput., 163 (2005), 373-381 ## M. M. Hosseini, Adomian decomposition method for solution of differential-algebraic equations, J. Comput. Appl. Math., 197 (2006), 373-381 ## M. M. Hosseini, Adomian decomposition method for solution of nonlinear differential algebraic equations, Appl. Math. Comput., 181 (2006), 1737-1744 ## J. H. He, Homotopy perturbation technique, Comput. Meth. Appl. Mech. Eng., 178 (1999), 257-262 ## J. H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Int. J. Nonlin. Mech., 35 (2000), 37-43 ## J. H. He, Approximate Solution of Nonlinear Differential Equations With Convolution Product Nonlinearities, Comput. Meth. Appl. Mech. Eng., 167 (1998), 69-73 ## H. Jafari, M. Zabihi, M. Saidy, Application of Homotopy-Perturbation Method for Solving Gas Dynamics Equation, Appl. Math. Sci., 2 (2008), 2393-2396 ## D. D. Ganji, The applications of He's homotopy perturbation method to nonlinear equation arising in heat transfer, Phy. Lett. A., 335 (2006), 337-3341 ## Y. Khan, An Effective Modification of the Laplace Decomposition Method for Nonlinear Equations, Int. J. Nonlinear Sci. Numer. Simul., 10 (2009), 1373-1376 ## M. Hussain, M. Khan, Modified Laplace Decomposition Method, Appl. Math. Sci., 4 (2010), 1769-1783 ## M. Khan, M. Hussain, Application of Laplace decomposition method on semi infinite domain, Numer. Algor., 56 (2011), 211-218 ## M. Khan, M. A. Gondal, New modified Laplace decomposition algorithm for Blasius flow equation, J. Adv. Res. Sci. Comput., 2 (2010), 35-43 ## M. Khan, M. A. Gondal, A new analytical solution of foam drainage equation by Laplace decomposition method, J. Adv. Res. Diff. Eqs., 2 (2010), 53-64 ## J. H. He, Approximate Analytical Solution for Seepage Flow with Fractional Derivatives in Porous Media, Comput. Meth. Appl. Mech. Eng., 167 (1988), 57-68 ## J. H. He, X.-H.Wu, Variational iteration method: new development and applications, Comput. Math. Appl., 54 (2007), 881-894 ## J. H. He, The variational iteration method for eighth-order initial-boundary value problems, Physica Scripta, 76 (2007), 680-682 ## J. H. He, Variational iteration method-a kind of non-linear analytical technique: some examples, Int. J. Nonlin. Mech., 34 (1999), 699-708 ## M. Hussain, M. Khan, A Variational Iterative Method for Solving the Linear and Nonlinear Klein-Gordon Equations , Appl. Math. Sci., 4 (2010), 1931-1940 ## H. Jafari, A. Yazdani, J. Vahidi, D. D. Ganji, Application of He's Variational Iteration Method for Solving Seventh Order Sawada-Kotera Equations, Appl. Math. Sci., 2 (2008), 471-477 ## H. Jafari, H. Tajadodi, He's Variational Iteration Method for Solving Fractional Riccati Differential Equation, Int. J. Diff. Eqs., 2010 (2010), 1-8 ## H. Jafari, M. Zabihi, E. Salehpoor, Application of variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations, Numer. Meth. Part. Diff. Eqs., 26 (2010), 1033-1039 ## H. Jafari, A. Alipoor, A new method for calculating general Lagrange multiplier in the variational iteration method, Numer. Meth. Part. Diff. Eqs., 27 (2011), 996-1001 ## H. Jafari, A. Golbabaib, E. Salehpoorc, Kh. Sayehvandb, Application of Variational Iteration Method for Stefan Problem, Appl. Math. Sci., 2 (2008), 3001-3004 ## G. A. Baker, Essentials of Padé Approximants, Academic Press, London (1975)
A Note on Non Linear Optimal Inventory Policy Involving Instant Deterioration of Perishable Items with Price Discounts A Note on Non Linear Optimal Inventory Policy Involving Instant Deterioration of Perishable Items with Price Discounts en en This paper derives a non linear optimal inventory policy involving instant deterioration of perishable items with allowing price discounts. This paper postulates that the inventory policy of perishable items very much resembles that of price discounts. Such a parallel policy suggests that improvements to production systems may be achievable by applying price discounts to increase demand rate of the perishable items. This paper shows how discounted approach reduces to perfect results, and how the post deteriorated discounted EOQ model is a generalization of optimization. The objective of this paper is to determine the optimal price discount, the cycle length and the replenishment quantity so that the net profit is maximized. The numerical analyses show that an appropriate discounted pricing policy can benefit the retailer and that discounted pricing policy is important, especially for deteriorating items. Furthermore the instant post deteriorated price discount crisp economic order quantity (CEOQ) model is shown to be superior in terms of profit maximization. The sensitivity analysis of parameters on the optimal solution is carried out. 145 155 M. Pattnaik Discounted selling price Instant deterioration Constant demand Inventory Article.6.pdf  D. S. Dave, K. E. Fitzapatrick, J. R. Baker, An advertising inclusive production lot size model under continuous discount pricing, Computational Industrial Engineering, 30 (1995), 147-159 ## K. Deb, Optimization for Engineering Design: Algorithms and Examples, Prentice-Hall, New Delhi (2000) ## P. M. Ghare, G. F. Schrader, A model for an exponentially decaying inventory, J. ind. Engng., 14 (1963), 238-243 ## S. Bose, A. Goswami, K. S. Chaudhuri, An EOQ model for deteriorating items with linear time dependent demand rate and shortages under inflation and time discounting, Journal of Operational Research Society, 46 (1995), 771-782 ## S. K. Goyal, B. C. Giri, Recent trends in modelling of deteriorating inventory, Eur. J. Oper. Res., 134 (2001), 1-16 ## M. Y. Jaber, M. Bonney, M. A. Rosen, I. Moualek, Entropic order quantity (EnOQ) model for deteriorating items, Applied mathematical modelling, 33 (2009), 564-578 ## M. J. Khouja, Optimal ordering, discounting and pricing in the single period problem, International Journal of Production Economics, 65 (2000), 201-216 ## L. Liu, D. H. Shi, An (s. S) model for inventory with exponential lifetimes and renewal demands, Naval Research Logistics, 46 (1999), 39-56 ## G. C. Mahata, A. Goswami, Production lot size model with fuzzy production rate and fuzzy demand rate for deteriorating item under permissible delay in payments, Opsearch, 43 (2006), 358-375 ## S. Pal, K. Goswami, K. S. Chaudhuri, A deterministic inventory model for deteriorating items with stock dependent demand rate, J. Prod. Econ., 32 (1993), 291-299 ## S. Panda, S. Saha, M. Basu, An EOQ model for perishable products with discounted selling price and stock dependent demand, Central European Journal of Operations Research, 17 (2009), 31-53 ## M. Pattnaik, An entropic order quantity model (EnOQ) under instant deterioration of perishable items with price discounts, International Mathematical Forum, 5 (2010), 2581-2590 ## F. Raafat, Survey of Literature on continuously deteriorating inventory model, Journal of Operational Research Society, 42 (1991), 27-37 ## N. H. Shah, Y. K. Shah, An EOQ model for exponentially decaying inventory under temporary price discounts, Cahiers du Centre d'études de recherche opérationnelle, 35 (1993), 227-232 ## E. A. Silver, R. Peterson, Decision system for inventory management and production Planning, John Wiley & Sons, New York (1985) ## K. Skouri, I. Konstantaras, S. Papachristos, I. Ganas, Inventory models with ramp type demand rate, partial backlogging and weibull deterioration rate, Eur. J. Oper. Res., Vol. 192, 79--92, (2009) ## P. K. Tripathy, M. Pattnaik, An fuzzy arithmetic approach for perishable items in discounted entropic order quantity model, International Journal of Scientific and Statistical Computing, 1 (2011), 7-19 ## P. K. Tripathy, M. Pattnaik, An entropic order quantity model with fuzzy holding cost and fuzzy disposal cost for perishable items under two component demand and discounted selling price, Pakistan Journal of Statistics and Operations Research, 4 (2008), 93-110 ## T. L. Urban, Inventory model with inventory level dependent demand a comprehensive review and unifying theory, Eur. J. Oper. Res., 162 (2005), 792-804 ## M. Vujosevic, D. Petrovic, R. Petrovic, EOQ formula when inventory cost is fuzzy, Int. J. Prod. Econ., 45 (1996), 499-504 ## L. R. Weatherford, S. E. Bodily, A taxonomy and research Overview of Perishable asset revenue management: yield management, overbooking, and pricing, Operations Research, 40 (1992), 831-844 ## H. M. Wee, S. T. Law, Replenishment and pricing policy for deteriorating items taking into account the time value of money, Int. J. Prod. Econ., 71 (2001), 213-220
Characterization the Deletable Set of Vertices in the (p-3)--Regular Graphs Characterization the Deletable Set of Vertices in the (p-3)--Regular Graphs en en In this paper we characterized the ( p - 3 )- regular graphs which have a 3−deletable and a 4−deletable set of vertices. 156 164 Akram B. Attar reducibility regular graphs dominating set and dominating number. Article.7.pdf  B. Attar Akram, B. N. Waphare, Reducibility of Eulerian Graphs and Digraphs, Journal of Al-Qadisiyah for Pure Science, 13 (2008), 183-194 ## G. Bordalo, B. Monjardet, Reducible classes of finite lattices, Order , 13 (1996), 379-390 ## J. Clark, D. A. Holton, A First Look at Graph Theory, World Scientific, London (1991) ## F. Harary , Graph Theory, Addison-Wesley, Reading (1969) ## V. S. Kharat, B. N. Waphare, Reducibility in finite posets, Europ. J. Combinatorics, 22 (2001), 197-205 ## P. J. Slater, Locating dominating sets and locating-dominating sets, In: Graph Theory, Combinatorics and Applications: Proceedings of the Seventh Quadrennial International Conference on the Theory and Applications of Graphs, 2 (1995), 1073-1079 ## W. T. Tutte, Graph Theory, Addison-Wesley, Reading (1984) ## D. B. West, Introduction to Graph Theory, Prentice Hall, Upper Saddle River (1999) ## L. W. Beineke, R. J. Wilson, Selected Topics in Graph Theory, Academic Press, London (1978)
Quasi-Permutation Representations for the Borel and Maximal Parabolic Subgroups of $$Sp(4,2^n)$$ Quasi-Permutation Representations for the Borel and Maximal Parabolic Subgroups of $$Sp(4,2^n)$$ en en A square matrix over the complex field with non-negative integral trace is called a quasi-permutation matrix.Thus every permutation matrix over C is a quasi-permutation matrix . The minimal degree of a faithful representation of G by quasi-permutation matrices over the complex numbers is denoted by c(G), and r(G) denotes the minimal degree of a faithful rational valued complex character of G . In this paper c(G) and r(G) are calculated for the Borel or maximal parabolic subgroups of $$SP(4,2^f)$$ . 165 175 M. Ghorbany General linear group Quasi-permutation. Article.8.pdf  H. Behravesh , Quasi-permutation representations of p-groups of class 2 , J. London Math. Soc., 55 (1997), 251-260 ## J. M. Burns, B. Goldsmith, B. Hartley, R. Sandling, On quasi-permutation representations of finite groups, Glasgow Math. J., 36 (1994), 301-308 ## M. R. Darafsheh, M. Ghorbany, A. Daneshkhah, H. Behravesh, Quasi-permutation representation of the group $$GL(2,q)$$, Journal of Algebra , 243 (2001), 142-167 ## M. R. Darafsheh, M. Ghorbany, Quasi-permutation representations of the groups $$SU (3, q^2)$$ and $$PSU(3,q^2 )$$, Southest Asian Bulletin of Mathemetics, 26 (2003), 395-406 ## M. R. Darafsheh, M. Ghorbany, Quasi-permutation representations of the groups $$SL(3,q)$$ and $$PSL(3,q)$$, Iranian Journal of Science and Technology Trans. A -Sci., 26 (2002), 145-154 ## H. Enomoto, The characters of the finite symplectic group $$SP(4, q), q = 2^f$$, Osaka J. Math., 9 (1972), 75-94 ## M. Ghorbany, Special representations of the group $$G_2(2^n)$$ with minimal degrees, Southest Asian Bulletin of Mathemetics , 30 (2006), 663-670 ## W. J. Wong, Linear groups analogous to permutation groups, J. Austral. Math. Soc. (Sec. A), 3 (1963), 180-184
On the Determination of Asymptotic Formula of the Nodal Points for Differential Pencils with Separated Boundary Conditions On the Determination of Asymptotic Formula of the Nodal Points for Differential Pencils with Separated Boundary Conditions en en In this work, we solve the inverse nodal problem for the diffusion operator on a finite interval with separated boundary conditions. We investigation the oscillation of the eigenfunctions and derive an asymptotic formula for the nodal points. Uniqueness theorem is proved, and a constructive procedure for the solution is provided. 176 178 A. Dabbaghian Sh. Akbarpoor Differential pencils Eigenvalues Eigenfunctions Nodal Points. Article.9.pdf  S. A. Buterin, C. T. Shieh, Inverse nodal problem for differential pencils, Appl. Math. Lett., 22 (2009), 1240-1247 ## H. Koyunbakan, A new inverse problem for the diffusion operator, Appl. Math. Lett., 19 (2006), 995-999
Fourth Order Volterra Integro-Differential Equations Using Modifed Homotopy-Perturbation Method Fourth Order Volterra Integro-Differential Equations Using Modifed Homotopy-Perturbation Method en en This paper compare modified homotopy perturbation method with the exact solution for solving Fourth order Volterra integro-differential equations. From the computational viewpoint, the modified homotopy perturbation method is more efficient and easy to use. 179 191 G. A. Afrouzi D. D. Ganji H. Hosseinzadeh R. A. Talarposhti Fourth order integro-differential equations modification of homotopy-perturbation method (MHPM) Nonlinear exact solution boundary value problems(BVP). Article.10.pdf  D. D. Ganji, G. A. Afrouzi, H. Hosseinzadeh, R. A. Talarposhti, Application of Hmotopy- perturbation method to the second kind of nonlinear integral equations, Physics Letters A, Vol. 371, 20--25, (2007) ## D. D. Ganji, A. Sadighi, Application of He's Homotopy-perturbation Method to Nonlinear Coupled Systems of Reaction-diffusion Equations, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 7, 411--418, (2006) ## D. D. Ganji, A. Rajabi, Assessment of homotopy-perturbation and perturbation methods in heat radiation equations, International Communications in Heat and Mass Transfer, 33 (2006), 391-400 ## D. D. Ganji, M. Rafei, Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method, Physics Letters A, 356 (2006), 131-137 ## J. H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng., 178 (1999), 257-262 ## J. H. He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Non-linear Mech., 35 (2000), 37-43 ## J. H. He, Limit cycle and bifurcation of nonlinear problems, Chaos Soliton. Fract., 26 (2005), 827-833 ## J. H. He, Homotopy perturbation method for bifurcation of nonlinear problems, Int. J. Nonlinear Sci. Numer. Simul., 6 (2005), 207-208 ## J. H. He, Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos Solitons Fractals, Vol. 19, 847--851 (2005) ## H. M. Liu, Variational approach to nonlinear electrochemical system, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 5, 95--96, (2004) ## J. H. He, Variational iteration method: a kind of nonlinear analytical technique: some examples, Int. J. Non-Linear Mech., 34 (1999), 699-708 ## J. H. He, Variational iteration method for autonomous ordinary differential systems , Appl. Math. Comput., 114 (2000), 115-123 ## J. H. He, X. H. Wu, Construction of solitary solution and compacton-like solution by variational iteration method, Chaos Solitons Fractals, 29 (2006), 108-113 ## M. El-Shahed, Application of He's homotopy perturbation method to Volterra's integro-differential equation, Int. J. Nonlinear Sci. Numer. Simul., 6 (2005), 163-168 ## J. H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B, 20 (2006), 1141-1199 ## J. H. He, A review on some new recently developed nonlinear analytical techniques, Int. J. Nonlinear Sci. Numer. Simul., 1 (2000), 51-70 ## S. Abbasbandy, Numerical solutions of the integral equations: homotopy perturbation method and Adomian's decomposition method, Appl. Math. Comput., 173 (2006), 493-500 ## S. Abbasbandy, Application of He's homotopy perturbation method to functional integral equations, Chaos Solitons Fractals, 31 (2007), 1243-1247 ## S. Abbasbandy, Application of He's homotopy perturbation method for Laplace transform, Chaos Solitons Fractals, 30 (2006), 1206-1212 ## J. H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals, 26 (2005), 695-700 ## J. H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities,, Appl. Math. Comput., 151 (2004), 287-292 ## J. H. He, Comparison of homotopy perturbation method and homotopy analysis method, Appl. Math. Comput., 156 (2004), 527-539 ## A. H. Nayfeh, Problems in Perturbation, John Wiley & Sons, New York (1985)
Solving Time Constrained Vehicle Routing Problem Using Hybrid Genetic Algorithm Solving Time Constrained Vehicle Routing Problem Using Hybrid Genetic Algorithm en en Vehicle Routing Problem with Time windows (VRPTW) is an example of scheduling in constrained environment. It is a well known NP hard combinatorial scheduling optimization problem in which minimum number of routes have to be determined to serve all the customers within their specified time windows. So far different analytic and heuristic approaches have been tried to solve such problems. In this paper we proposed algorithms which incorporate new local search techniques with genetic algorithm approach to solve VRPTW scheduling problems in various scenarios. 192 201 Bhawna Minocha Saswati Tripathi Genetic algorithm heuristics based search techniques vehicle routing problem with time windows case- study Article.11.pdf  J. Berger, M. Barkaoui, A parallel hybrid genetic algorithm for the vehicle routing problem with time windows, Computer Operation Research, 31 (2004), 2037-2053 ## J. L. Blanton, R. L. Wainwright, Multiple vehicle routing with time and capacity constraints using genetic algorithms, Proceedings of the 5th International Conference on Genetic Algorithms, 1993 (1993), 452-459 ## O. Bräysy, M. Gendreau, Vehicle routing problem with time windows Part II: Metaheuristics, Transportation Science, 39 (2005), 119-139 ## A. Chabrier , Vehicle Routing Problem with Elementary Shortest Path based Column Generation, Computers and Operations Research, 33 (2006), 2972-2990 ## J. F. Cordeau, G. Laporte, A. Mercier, A unified tabu search heuristic for vehicle routing problems with time windows, Journal of the Operational Research Society, 52 (2001), 928-936 ## J. F. Cordeau, G. Desaulniers, J. Desrosiers, M. M. Solomon, F. Soumis, The VRP with Time Windows, in: The Vehicle Routing Problem, 2002 (2002), 157-193 ## L. M. Gambardella, E. Taillard, G. Agazzi, MACS-VRPTW: A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows, in: New Ideas in Optimization, 63--76, U. K. (1999) ## J. H. Holland, Adaptation in natural and artificial systems: an introductory analysis with application to biology, University of Michigan Press, Ann Arbor (1975) ## J. Hömberger, H. Gehring, A Two-Phase Hybrid Metaheuristic for the Vehicle Routing Problem with Time Windows, Eur. J. Oper. Res., 162 (2005), 220-238 ## B. Kallehauge, J. Larsen, O. B. G. Madsen, Lagrangean duality and non-differentiable optimization applied on routing with time windows, Computers and Operations Research, 33 (2006), 1464-1487 ## N. Kohl, J. Desrosiers, O. B. G. Madsen, M. M. Solomon, F. Soumis, 2-Path Cuts for the Vehicle Routing Problem with Time Windows, Transportation Science, 33 (1999), 101-116 ## J. Larsen , Parallelization of the vehicle routing problem with time windows, Ph.D. Thesis (Technical University of Denmark), Denmark (1999) ## B. Ombuki, B. J. Ross, F. Hansher, Multi-objective Genetic Algorithm for Vehicle Routing Problem with Time Windows, Applied Intelligence, 24 (2006), 17-30 ## B. Minocha, S.Tripathi, Vehicle Routing Problem with Time Windows: An Evolutionary Algorithmic Approach, Algorithmic Operations Research, 1 (2006), 1-15 ## J. Potvin, S. Bengio, The Vehicle Routing Problem with Time Windows part II: Genetic Search, INFORMS Journal on Computing, 8 (1996), 165-172 ## Y. Rochat, E. Taillard, Probabilistic Diversification and Intensification in Local Search for Vehicle Routing, Journal of Heuristics, 1 (1995), 147-167 ## S. Ropke, D. Pisinger, A General Heuristics for Vehicle Routing Problems, Computers & Operations Research, 34 (2007), 2403-2435 ## P. Shaw, Using Constraint Programming and Local Search Methods to solve Vehicle Routing Problems, International conference on principles and practice of constraint programming, 1998 (1998), 417-431 ## M. M. Solomon, Algorithms for Vehicle Routing and Scheduling Problems with Time Window Constraints, Operations Research, 35 (1987), 254-265 ## E. D. Taillard, P. Badeau, M. Gendreau, F. Guertin, J. Potvin, A Tabu Search Heuristics for the Vehicle Routing Problem with Soft Time Windows, Transportation Science, 31 (1997), 170-186 ## K. C. Tan, L. H. Lee, K. Ou, Hybrid Genetic Algorithms in Solving Vehicle Routing Problems with Time Window Constraint, Asia-Pacific Journal of Operation Research, 18 (2001), 121-130 ## S. R. Thangiah, Vehicle Routing with Time Windows using Genetic Algorithms, In: Application Handbook of Genetic Algorithms: New Frontiers, 1995 (1995), 253-277
Mathematical Modeling of Corrosion Phenomenon in Pipelines Mathematical Modeling of Corrosion Phenomenon in Pipelines en en The annual cost of corrosion worldwide is over 3% of the world’s GDP. There are hundreds of thousands of kilometers of pipelines in various sectors of industry, which include many uncoated pipelines in chemical manufacturing plants, interstate natural gas transmission lines, and offshore oil-and-gas production pipelines. Mathematical modeling is richly endowed with many analytic computational techniques for analyzing real life situations. This paper reviewed that the predictive models on corrosion rate for natural gas pipeline. These models were selected based on the thermodynamic properties of the fluid and the developed rate is plotted against various operating conditions. 202 211 M. R. Sarmasti Emami Iran University of Science & Technology Mathematical models Corrosion rate Pipeline Article.12.pdf  S. O. Ale, Curriculum development in modelling process, International Centre for Theoretical Physics occasional publication, Trieste, Italy, SMR, 99 (1981), 1-42 ## S. O. Ale, Encouraging the Teaching of mathematical modelling in Nigerian schools, Nigerian Education Forum, 9 (1986), 185-191 ## Morton Daniel, Mathematically Speaking, Harcourt Brace, Jovanovich, Inc, New York (1980) ## M. R. Sarmasti Emami, Investigation of probability corrosion in metallic stack by sulfuric acid, The 11th Iranian Corrosion Conference, , 12-14 May, Kerman Iran, (2009), 489-499 ## M. R. Sarmasti Emami, M. Zahedi, Investigation of Causes of Corrosions in Pipe Supports: A Case Study in Amir Kabir Semisubmersible Drilling Unit, The 9th Iranian Biennial Electrochemistry Conference, (2011), 1-145 ## M. R. Sarmasti Emami, M. Nematti, M. Zahedi, Z. Jamal Ara, Causes of Corrosion the Air Preheater in Neka Power Plant, The 9th Iranian Biennial Electrochemistry Conference, 22-24 Jan, Yazd , Iran, (2011), 1-145 ## Corrosion Prevention, Control /UK, British standard for corrosion protection, No 2, Jul 26, Last Modified, 14 (1994), 7-8 ## Berry John, Mathematical modeling: A Source Book of Case Studies, Edited by I.D Huntley and D.J.G James, Oxford University Press London, (1990), 81-96 ## S. Beddling , Concerning an integral arising in the study of laser - Drilling Equation, International Journal of Science Technology, 25 (1994), 609-672 ## O. B. Oyelami, A. A. Asere, Mathematical modeling: an Application to corrosion in a petroleum industry, National Mathematical Centre Abuja, Nigeria () ## H. Uthmana, Mathematical Modeling and Simulation of Corrosion Processes in Nigerian Crude Oil Pipelines, Journal of Dispersion Science and Technology, 32 (2011), 609-615 ## X. Cheng, Y. Bo, Z. Zhengwei, Z. Jinjun, W. Jinjia, S. Shuyu, Numerical simulation of a buried hot crude oil pipeline during shutdown, Pet.Scienc., 7 (2010), 73-82 ## Pierre R. Roberge, Handbook of Corrosion, Chapter 11, McGraw-Hill, (1999), 863-904 ## N. P. Glazov, Underground Corrosion of Pipelines, Its Prediction and Diagnostics, Gasprom, Moscow, Russia (1994) ## A. M. Bolotnov, N. N. Glazov, N. P. Glazov, K. L. Shamshetdinov, V. D. Kiselev, Mathematical Model and Algorithm for Computing the Electric Field of Pipeline Cathodic Protection with Extended Anodes, Protection of Metals , 44 (2008), 408-411
Modification of the Homotopy Perturbation Method for Numerical Solution of Nonlinear Wave and System of Nonlinear Wave Equations Modification of the Homotopy Perturbation Method for Numerical Solution of Nonlinear Wave and System of Nonlinear Wave Equations en en In this paper, the modification of the homotopy perturbation method (MHPM) Zaid M. Odibat (Appl. Math. Comput. 2007 ) is extended to derive approximate solutions of the nonlinear coupled wave equations. This work will present a numerical comparison between the modification and the homotopy perturbation method (HPM). In order to show the ability and reliability of the method some examples are provided. The results reveal that the method is very effective and simple. The modified method accelerates the rapid convergence of the series solution and reduces the size of work. 212 224 B. Ghazanfari A. G. Ghazanfari M. Fuladvand Homotopy purturbation method Nonlinear differential equations Modified homotopy perturbation method Homotopy purturbation method Nonlinear differential equations Modified homotopy perturbation method Article.13.pdf  J. H. He, An approximate solution technique depending on an artificial parameter: A special example, Commun. Nonlinear Sci. Numer. Simul., 3 (1998), 92-97 ## S. Abbasbandy, Iterated He's homotopy perturbation method for quadratic Riccati differential equation, Appl. Math. Comput., 175 (2006), 581-589 ## S. Abbasbandy, Application of He's homotopy perturbation method to functional integral equations, Chaos Solitons Fractals, 31 (2007), 1243-1247 ## J. H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals, 26 (2005), 695-700 ## D. D. Ganji, A. Sadighi, Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations, Int. J. Nonlinear Sci. Numer. Simul., 7 (2006), 411-418 ## H. Jafari, S. Seifi, Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation, Commun. Nonli. Science Numer. Simul., 14 (2009), 2006-2012 ## H. Jafari, M. Zabihi, M. Saidy, Application of homotopy perturbation method for solving gas dynamics equation, Appl. Math. Sci., 2 (2008), 2393-2396 ## M. Javidi, A. Golbabai, A numerical solution for solving system of Fredholm integral equations by using homotopy perturbation method, Appl. Math. Comput., 189 (2007), 1921-1928 ## J. I. Ramos, Piecewise homotopy methods for nonlinear ordinary differential equations, Appl. Math. Comput., 198 (2008), 92-116 ## Q. Wang, Homotopy perturbation method for fractional KdV equation, Appl. Math. Comput., 190 (2007), 1795-1802 ## Z. M. Odibat, A new modification of the homotopy perturbation method for linear and nonlinear operators, Appl. Math. Comput., 189 (2007), 749-753 ## M. Ghasemi, M. T. Kajani, A. Davari, Numerical solution of two-dimensional nonlinear differential equation by homotopy perturbation method, Appl. Math. Comput., 189 (2007), 341-345 ## P. Roul, P. Meyer, Numerical solutions of systems of nonlinear integro-differential equations by Homotopy-perturbation method, Appl. Math. Model., 35 (2011), 4234-4242 ## J. Singh, P. K. Gupta, K. N. Rai, Homotopy perturbation method to space–time fractional solidification in a finite slab, Appl. Math. Model., 35 (2011), 1937-1945 ## K. A. Gepreel, The homotopy perturbation method applied to the nonlinear fractional Kolmogorov–Petrovskii–Piskunov equations, Appl. Math. Letters, 24 (2011), 1428-1434 ## A. M. Wazwaz, Necessary conditions for the appearance of noise terms in decomposition solution series, J. Math. Anal. Appl., 5 (1997), 265-274 ## J. H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Eng., 167 (1998), 57-68
Numerical Solution for Maxwells Equation in Metamaterials by Homotopy Analysis Method Numerical Solution for Maxwells Equation in Metamaterials by Homotopy Analysis Method en en In this paper, the Homotopy analysis Method (HAM) is applied to the Maxwell system. The HAM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. 225 235 A. Zare M. A. Firoozjaee Homotopy analysis Method Maxwell system Article.14.pdf  G. Adomian , Coupled Maxwell Equations for Electromagnetic Scattering, Applied Mathemathics and Compution, 77 (1996), 133-135 ## J. H. He , Homotopy perturbation method for solving boundary value problems, Phys. Lett. A, 350 (2006), 87-88 ## J. H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B, 20 (2006), 1141-1199 ## J. Li, Numerical convergence and physical fidelity analysis for Maxwell's equations in metamaterials, Comput. Methods Appl. Mech. Engrg., 198 (2009), 3161-3172 ## H. Jafari, M. Saeidy, M. A. Firoozjaee, The Homotopy Analysis Method for Solving Higher Dimensional Initial Boundary Value Problems of Variable Coefficients, Numerical Methods for Partial Differential Equations, Numerical Methods for Partial Differential Equations, 26 (2010), 1021-1032 ## H. Jafari, M. A. Firoozjaee , Multistage Homotopy Analysis Method for Solving Nonlinear Integral Equations, Appl. Appl. Math. Int. J., 1 (2010), 34-35 ## S. J. Liao , Beyond perturbation: introduction to the homotopy analysis method, Chapman & Hall/CRC Press, Boca Raton (2003) ## S. J. Liao , The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis (Shanghai Jiao Tong University), Shanghai (1992) ## S. J. Liao, On the homotopy analysis method for nonlinear problems, Appl. Math. Comput., 147 (2004), 499-513 ## V. Dolean, S. Lanteri, R. Perrussel, A domain decomposition method for solving thethree-dimensional time-harmonic Maxwell equations discretized by discontinuous Galerkin methods, Journal of Computational Physics, 227 (2008), 2044-2072
Estimating the Average Worth of a Subset Selected from Binomial Populations Estimating the Average Worth of a Subset Selected from Binomial Populations en en Suppose $$\overline{X}=(\overline{X}_1,...\overline{X}_p), (p\geq 2)$$; where $$\overline{X}_i$$represents the mean of a random sample of size ni drawn from binomial $$bin(1,\theta_i)$$ population. Assume the parameters $$\theta_1,...,\theta_p$$ are unknown and the populations $$bin(1,\theta_1),...,bin(1,\theta_p)$$ are independent. A subset of random size is selected using Gupta's (Gupta, S. S. (1965). On some multiple decision(selection and ranking) rules. Technometrics 7,225-245) subset selection procedure. In this paper, we estimate of the average worth of the parameters for the selected subset under squared error loss and normalized squared error loss functions. First, we show that neither the unbiased estimator nor the risk- unbiased estimator of the average worth (corresponding to the normalized squared error loss function) exist based on a single-stage sample. Second, when additional observations are available from the selected populations, we derive an unbiased and risk-unbiased estimators of the average worth and also prove that the natural estimator of the average worth is positively biased. Finally, the bias and risk of the natural, unbiased and risk-unbiased estimators are computed and compared using Monti Carlo simulation method. 236 245 Riyadh Al-Mosawi binomial populations selected subset average worth estimation Article.15.pdf  R. Al-Mosawi, P. Vellaisamy, A. Shanubhogue, Risk-Unbiased estimation of the selected subset of Poisson populations, Journal of Indian Statistical Association, Vol. 49, (2011) ## R. R. Al-Mosawi, A. Shanubhogue, P. Vellaisamy, Average worth estimation of the selected subset of Poisson populations, Statistitcs, 46 (2012), 813-831 ## J. D. Gibbons, I. Olkin, M. Sobel, Selecting and ordering populations: a new statistical methodology.Society for Industrial and Applied Mathematics (SIAM), SIAM, Philadelphia (1999) ## S. S. Gupta, On some multiple decision (selection and ranking) rules, Technometrics, 7 (1965), 225-245 ## S. S. Gupta, S. Panchapakesan, Multiple decision procedures: theory and methodology of selection and ranking populations. Society for Industrial and Applied Mathematics (SIAM), SIAM, Philadelphia (2002) ## S. Jeyarathnam, S. Panchapakesan, An estimation problem relating to subset selection for normal populations, Design of Experiments: Ranking and Selection (Technical rept.), New York (1983) ## S. Jeyarathnam, S. Panchapakesan, Estimation after subset selection from exponential populations, Communications in Statistics-Theory and Methods, 15 (1986), 3459-3473 ## S. Kumar, A. K. Mahapatra, P. Vellaisamy, Relaibility estimation of the selected exponential populations, Statistics & Probability Letters, 52 (2009), 305-318 ## E. L. Lehmann, G. Casella, Theory of point estimation, Springer-Verlag, New York (1998) ## P. Vellaisamy, Average worth and simulatneous estimation of the selected subset, Ann. Inst. Statist. Math., 44 (1992), 551-562 ## P. Vellaisamy, On UMVUE estimation following selection, Comm. Statist--Theory Methods, 22 (1993), 1031-1043 ## P. Vellaisamy, Simultaneous estimation of the selected subset of uniform populations, J. Appl. Statist.Sci., 5 (1996), 39-46 ## P. Vellaisamy, R. R. Al-Mosawi, Simultaneous estimation of Poisson means of the selected subset, J. Statist. Plann. Infer., 140 (2010), 3355-3364
A Remark on the Coupled Fixed Point Theorems for Mixed Monotone Operators in Partially Ordered Metric Spaces A Remark on the Coupled Fixed Point Theorems for Mixed Monotone Operators in Partially Ordered Metric Spaces en en We present a coupled fixed point theorems for mixed monotone operators in partially ordered metric spaces. 246 261 S. H. Rasouli M. Bahrampour Coupled fixed point Partially ordered set Mixed monotone operators. Article.16.pdf  A. Amini-Harandi, H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Analysis: Theory, Methods & Applications, 72 (2010), 2238-2242 ## J. Harjani, B. Lpez, K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Analysis: Theory, Methods & Applications, 74 (2011), 1749-1760 ## T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaced and applications, Nonlinear Analysis: Theory, Methods & Applications, 65 (2006), 1379-1393 ## R. P. Argarwal, M. A. El-Gebeily, D. O'Regan, Generalized contraction in partially ordered metric spaces, Appl. Anal., 87 (2008), 109-116 ## D. Burgić, S. Kalabušić, M. R. S. Kulenović, Global attractivity results for mixed monotone mappings in partially ordered complete metric spaces, Fixed Point Theory Appl., 17 pages, (2009) ## L. Ciric, N. Cakid, M. Rajovic, J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Ponit Theory Appl., 11 pages, (2008) ## J. Harjani, K. Sadarangani, Fixed point theorems for weakly contractive mapings in partially ordered sets, Nonlinear Analysis: Theory, Methods & Applications, 71 (2009), 3403-3410 ## J. Harjani, K. Sadarangani, Generalized contraction in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Analysis: Theory, Methods & Applications, 72 (2010), 1188-1197 ## J. Harjani, K. Sadarangani, Fixed Point Theorems for Mappings satisfying a condition of integral type in partially ordered set, Journal of Convex Analysis, Vol. 17, 597--609, (2010) ## V. Lakshmikantham, L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. , 70 (2009), 4341-4349 ## J. J. Nieto, R. Rodriguez-Lopez, Existence of extremal solutions for quadratic fuzzy equations, Fixed Point Theory Appl., 2005 (2005), 321-342 ## J. J. Nieto, R. Rodriguez-Lopez, Contractive mappings theorem in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239 ## J. J. Nieto, R. Rodriguez-Lopez, Applications of contractive-like mapping principles to fuzzy equations, Rev. Math. Complut., 19 (2006), 361-383 ## J. J. Nieto, R. L. Pouso, R. Rodriguez-Lopez, Fixed point theorems in ordered abstract spaces, Proc. Amer.Math. Soc., 135 (2007), 2505-2517 ## J. J. Nieto, R. Rodriguez-Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica, 23 (2007), 2205-2212 ## D. O'Regan, A. Petrusel, Fixed point theorems for generalized contraction in oerdered metric spaces, J. Math. Anal. Appl., 341 (2008), 1241-1252 ## A. Petrusel, I. A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc., 134 (2006), 411-418 ## A. C. M. Ran, M. C. B. Reurings, A fixed point theorems in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1432-1443 ## Z. Drici, F. A. Mcrae, J. V. Devi, Fixed point theorems in partially ordered metric spaces for operators with PPF dependence, Nonlinear Analysis: Theory, Methods & Applications, 7 (2007), 641-647 ## Y. Wu, New fixed point theorems and applications of mixed monotone operator, J.Math. Anal. Appl., 341 (2008), 883-393 ## A. Cabada, J. J. Nieto, Fixed point and approximate solutions for nonlinear operator equations, J. Comput. Appl. Math., 113 (2000), 17-25 ## M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distanced between the points, Bull. Austral. Math. Soc., 30 (1984), 1-9 ## M. A. Geraghty, On contractive mappings, Proc. Amer. Math. Sox., 40 (1973), 604-608 ## D. Guo, V. Lakshmikantham, Coupled fixed point of nonlinear operators with applicatons, Non-Linear Analysis, 11 (1987), 623-632 ## D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New York (1988) ## D. 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The Nehari Manifold for a Quasilinear Elliptic Equation with Singular Weights and Nonlinear Boundary Conditions The Nehari Manifold for a Quasilinear Elliptic Equation with Singular Weights and Nonlinear Boundary Conditions en en Using the technique of Brown and Wu ; we present a note on the paper  by Wu. Indeed, we extend the multiplicity results for a class of semilinear problems to the quasilinear elliptic problems with singular weights of the form: $\begin{cases} -div(|x|^{-ap}|\nabla u|^{p-2}\nabla u)\lambda|x|^{-(a+1)p+c}f(x)|u|^{q-2}u,\,\,\,\,\, x\in \Omega,\\ |\nabla u|^{p-2} \frac{\partial u}{\partial n}=|x|^{-(a+1)p+c}g(x)|u|^{r-2}u, \,\,\,\,\, x\in \partial \Omega. \end{cases}$ Here $$0\leq a<\frac{N-p}{p}, c$$ is a positive parameter, $$1 < q < p < r < p*(p* = \frac{pN}{N-p}$$ if $$N > p, p* =\infty$$ if $$N \leq p), \Omega\subset R^N$$ is a bounded domain with smooth boundary, $$\frac{\partial }{\partial n}$$ is the outer normal derivative, $$\lambda\in R-{0}$$; and $$f(x); g(x)$$ are continuous functions which change sign in $$\overline{\Omega}$$. 262 277 S. H. Rasouli K. Fallah Quasilinear elliptic problem Singular weights Nehari manifold Nonlinear boundary condition. Article.17.pdf  C. O. Alves, A. El Hamidi, Nehari manifold and existence of positive solutions tob a class of quasilinear problems, Nonlinear Analysis: Theory, Methods & Applications, 60 (2005), 611-624 ## A. Ambrosetti, H. Brezis, G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal., 122 (1994), 519-543 ## H. Amman, J. Lopez-Gomez, A priori bounds and multiple solution for superlinear indefinite elliptic problems, J. Differential Equations, 146 (1998), 336-374 ## D. Arcoya, J. I. Diaz, S-shaped bifurcation branch in a quasilinear multivalued model arising in climatology, J. Differential Equations, 150 (1998), 215-225 ## C. Atkinson, K. El-Ali, Some boundary value problems for the Bingham model, J. Non-Newtonian Fluid Mech., 41 (1992), 339-363 ## C. Atkinson, C. R. Champion, On some boundary value problems for the equation $$\nabla(F(|\nabla w|)\nabla w)=0$$, Proc. R. Soc. Lond. A, 448 (1995), 269-279 ## P. A. Binding, Y. X. Huang, P. 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