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

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Résumé

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.

Mots-clés

Dirichlet problem, p(x)-Laplacian, variable exponent, weak solutions, multiplicity of solutions, variable exponent Sobolev spaces, mountain pass lemma, nontrivial solutions