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

TL;DR

This paper establishes the existence of solutions for a nonlinear anisotropic difference equation involving a p(k)-Laplacian operator using variational methods and local minimum theorems.

Contribution

It introduces a novel application of variational methods and local minimum theorems to analyze p(k)-Laplacian difference equations with Dirichlet boundary conditions.

Findings

Existence of non-trivial solutions proven for the nonlinear p(k)-Laplacian difference equation.

Application of Bonanno's local minimum theorems to discrete nonlinear problems.

Advancement in analytical techniques for anisotropic discrete boundary value problems.

Abstract

In the present paper, by using variational method, the existence of non-trivial solutions to an anisotropic discrete non-linear problem involving p(k)-Laplacian operator with Dirichlet boundary condition is investigated. The main technical tools applied here are the two local minimum theorems for differentiable functionals given by Bonanno.