Existence of a non-trivial solution for nonlinear difference equations

Abstract

Abstract. The existence of a non-trivial solution for a discrete non-linear Dirichlet problem involving p -Laplacian is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Bonanno.Mathematics subject classification (2010): 39A10, 34B15.

Multiple Solutions of a Discrete Nonlinear Boundary Value Problem Involving p(k)-Laplace Kirchhoff Type Operator

“…Our first tool and approach is based on a local minimum theorem due to Bonanno [7, Theorem 5.1], which is inspired by the Ricceri variational principle (see [47,Theorem 2.5] ). We refer the readers to the papers [3,6,8,9,26,40] in which Theorem 2.5 below have been successfully employed to get the existence of at least one nontrivial solution for boundary value problems.…”

Infinitely Many Positive Solutions for a Coupled Discrete Boundary Value Problem

“…More recently, especially, in [23][24][25][26][27][28][29][30][31], by starting from the seminal papers [32,33], many results for the existence and multiplicity of solutions for discrete boundary value problems have been obtained also by adopting variational methods.…”

Existence results to a nonlinear p(k)-Laplacian difference equation

“…In this context, anisotropic discrete nonlinear problems involving p(k)-Laplacian operator seem to have attracted a great deal of attention due to its usefulness of modelling some more complicated phenomenon such us fluid dynamics and nonlinear elasticity. We refer the reader to [1,2,3,4,5,6,7,9,12,13,14,16,17,18,19,20,21,22,24] and references therein, where they could find the detailed background as well as many different approaches and techniques applied in the related area.…”