MMN-4101

# Existence of solution for a Dirichlet boundary value problem involving the p(x) Laplacian via a fixed point approach

*Souad Ayadi*;

*Ozgur Ege*;

## Abstract

In this paper, we study the existence of a non-trivial solution in $W_{0}^{1,p(x)}(\Omega)$ for the problem
$$\begin{cases}\Delta_{p(x)}u=f(x,u,\nabla u) \;\;{\rm in}\quad \Omega,\\
u=0\;\;{\rm in}\quad \Omega.\end{cases}$$
The proof is based on Schaefer's fixed point theorem.

Vol. 23 (2022), No. 1, pp. 85-92

DOI: 10.18514/MMN.2022.4101