Non-homogeneous Dirichlet problems with concave-convex reaction

Abstract

— The variational methods are adopted for establishing the existence of at least two nontrivial solutions for a Dirichlet problem driven by a non-homogeneous di¤erential operator of p-Laplacian type. A large class of nonlinear terms is considered, covering the concave-convex case. In particular, two positive solutions to the problem are obtained under a ðp 1Þ-superlinear growth at infinity, provided that a behaviour less than ðp 1Þ-linear of the nonlinear term in a suitable set is requested.