Existence of solutions for p(x)-Laplacian Dirichlet problem by topological degree

Abstract

In this paper, we prove the existence of at least one solution for the Dirichlet problem of p(x)-Laplacian -div(|∇u|^p(x)-2∇u) = f(x; u; ∇u); by using the topological degree theory for a class of demicontinuous operators of generalized (S+) type. The right-hand side f is a Caratheodory function satisfying some non-standard growth conditions.