Boletim da Sociedade Paranaense de Matemática (May 2024)
Multiplicity of solutions for anisotropic Dirichlet problem with variable exponent
Abstract
We establish some results on the existence of multiple nontrivial solutions for a general anisotropic elliptic equations. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with adequate variational methods and a variant of the Mountain Pass lemma.