Multiple solutions for a parametric Steklov problem involving the $p(x)$-Laplacian operator

Abstract

In this paper, we study the existence and multiplicity of weak solutions for a Steklov problem involving $p(x)$-Laplacian operator in a bounded domain $\Omega \subset \mathbb{R}^N\ (N\geq2)$ with smooth boundary $\partial \Omega$. The boundary equation is perturbed with some weight functions belonging to approriate generalized Lebesgue spaces and two real parameters. Our arguments are based on variational method, using "Mountain Pass Theorem", "Fountain Theorem" and "Dual Fountain Theorem" combined with the critical points theory, we prove several existence results.

Keywords

• steklov problem
• $p(x)$-laplacian operator
• generalized lebesgue-sobolev spaces
• variational method
• mountain pass theorem
• fountain theorem
• dual fountain theorem