Multiplicity result for Dirichlet problem driven by p(x)- Laplacian-like operator

Abstract

We prove the existence and multiplicity of nontrivial weak solutions for a class of Dirichlet problems involving a p(x)-Laplacian-like operator. The study is conducted in the setting of variable exponent Sobolev spaces and employs appropriate variational methods together with a variant of the Mountain Pass Lemma.