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 differential 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 $(p-1)$-superlinear growth at infinity, provided that a behaviour less than $(p-1)$-linear of the nonlinear term in a suitable set is requested.