Nontrival solution for nonlinear p(x)-Laplacian Dirichlet problem with the sign-changing weight

TL;DR

This paper establishes conditions for the existence of solutions to a nonlinear elliptic p(x)-Laplacian problem with sign-changing weights using critical point theory for nonsmooth functionals.

Contribution

It introduces new existence results for nonlinear p(x)-Laplacian problems with sign-changing weights employing advanced critical point theory.

Findings

Existence of solutions under certain conditions

Application of critical point theory to nonsmooth potentials

Handling of sign-changing weight functions

Abstract

In this paper we study the nonlinear elliptic problem involving p(x)-Laplacian with nonsmooth potential, where the weighted function may change sign. By using critical point theory for locally Lipschitz functionals due to Chang, we obtain conditions which ensure the existence of a solution for our problem.