Solutions for the P(x)-Laplacian With Dependence on the Gradient

Abstract

This paper is concerned with the existence of nontrivial solutions for p(x)-Laplacian equations with gradient dependence − div |∇u| p(x)−2 ∇u + |u| p(x)−2 u = f (x, u, |∇u| p(x)−2 ∇u) in Ω, u = 0 on ∂Ω, (P) The techniques are based on an iterative scheme of Mountain Pass "approximated" solutions.