Second order discrete boundary value problem with the $(p_1(k); p_2(k))$-Laplacian
Résumé
In this paper we investigate existence and non-existence of solutions for a Dirichlet boundary value problem involving the $(p_1(k), p_2(k))$-Laplacian operator when variational methods are applied to obtain the results.
Téléchargements
Références
R. P. Agarwal, K. Perera, D. O’Regan, Multiple positive solutions of singular discrete p-Laplacian problems via variational methods, Adv. Difference Equ. 2, 93–99, (2005).
A. Ambrosetti, H. Rabinowitz, Dual variational methods in critical point theory, J. Funct. Anal. 14, 349–381, (1973).
M. Allaoui, O. Darhouche, Existence and multiplicity results for Dirichlet boundary value problems involving the (p1(x); p2(x))-Laplace operator, Note di Matematica, 37, 69-86, (2017).
L. H. Bian, H. R. Sun, Q. G. Zhang, Solutions for discrete p−Laplacian periodic boundary value problems via critical point theory, J. Difference Equ. Appl. 18, 345-355, (2012 ).
X. Cai, J. Yu, Existence theorems for second-order discrete boundary value problems, J. Math. Anal. Appl. 320, 649-661, (2006).
Y. Chen, S. Levine, M. Rao, Variable exponent, linear growth functionals in image processing, SIAM J. Appl. Math. 66, 1383-1406, (2006).
X. L. Fan, D. Zhao, On the spaces Lp(x) and Wm;p(x), J. Math. Anal. Appl. 263, 424-446, (2001).
X. L. Fan, Q. H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problem, Nonlinear Anal. 52, 1843-1852, (2003).
M. Galewski, R. Wieteska, Existence and multiplicity of positive solutions for discrete anisotropic equations, Turk. J. Math, 38, 297-310, (2014).
P. Harjulehto, P. Hasto, U.V. Lê, M. Nuortio, Overview of differential equations with non-standard growth, Nonlinear Anal. 72, 4551-4574, (2010).
B, Kone , S. Ouaro, Weak solutions for anisotropic discrete boundary value problems, J. Difference Equ. Appl. 17, 1537-1547, (2011).
S. B. Liu, S. J. Li, Infinitely many solutions for a superlinear elliptic equation, Acta Math. Sinica, 46, 625-630, (2003).
J. Liu, J. Su, Remarks on multiple nontrivial solutions for quasi-linear resonant problemes. J. ath. Anal. Appl.258, 209-222, (2001).
D. Liu, X. Wang, J. Yao, On (p1(x); p2(x))-Laplace equations, arXiv:1205.1854v1, (2012).
M. Mihailescu, V. Radulescu, S. Tersian, Eigenvalue problems for anisotropic discrete boundary value problems, J. Difference Equ. Appl. 15, 557-567, (2009).
M. Ruzicka, Electrorheological fluids: Modelling and Mathematical Theory, In Lecture Notes in Mathematics, 1748, Berlin: Springer-Verlag, (2000).
J. Smejda, R. Wieteska On The Dependence On Parameters For Second Order Discrete Boundary Value Problems With The p(k)-Laplacian, Opuscula Math. 34, 851–870, (2014).
P. Stehlik, On variational methods for periodic discrete problems. J. Difference Equ. Appl. 14, 259-273, (2008).
Y. Tian, Z. Du, W. Ge, Existence results for discrete Sturm-Liouville problem via variational methods. J. Difference Equ. Appl. 13, 467-478, (2007).
M. Willem, Mountain pass theorem, Minimax Theorem, Birkhäuser Boston, 7-36, (1996).
A. Zang, p(x)-Laplacian equations satisfying Cerami condition, J. Math. Anal. Appl. 337, 547-555, (2008).
J. Zhao, Structure theory of Banach spaces, Wuhan Univ. Press, Wuhan, (1991).
X. Zhang , X. Tang, Existence of solutions for a nonlinear discrete system involving the p-Laplacian, Appl. Math. 57, 11-30, (2012).
V. V. Zhikov , Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR Izv. 29, 33-66, (1987).
W. Zou, Variant fountain theorems and their applications, Manuscripta Mathematica, 104, 343-358, (2001).
Copyright (c) 2024 Boletim da Sociedade Paranaense de Matemática

Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).