Existence of solution for Dirichlet problem with p(x)-Laplacien

Abstract

In this paper we study an elliptic equation involving the p(x)-Laplacien operateur, for that equation we prove the existence of a non trivial weak solution. The proof relies on simple variational arguments based on the Mountain-Pass theorem.

Keywords

• p(x)-Laplacien
• Generalized Lebesgue (Sobolev) spaces
• Critical points