Existence result for differential inclusion with p(x)-Laplacian

TL;DR

This paper establishes the existence of solutions for a nonlinear elliptic problem involving the p(x)-Laplacian, using critical point theory for locally Lipschitz functionals, advancing understanding of hemivariational inequalities.

Contribution

It provides a new existence result for differential inclusions with p(x)-Laplacian using critical point theory, which was not previously applied to this problem.

Findings

Existence of a nontrivial solution for the p(x)-Laplacian problem.

Application of critical point theory to hemivariational inequalities.

Advancement in solving nonlinear elliptic problems with variable exponent Laplacian.

Abstract

In this paper we study the nonlinear elliptic problem with p(x)-Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to Chang.