Solutions of nonlinear nonhomogeneous Neumann and Dirichlet problems

Abstract

We consider nonlinear Neumann and Dirichlet problems driven by a nonhomogeneous differential operator and a Caratheodory reaction. Our framework incorporates $p$-Laplacian equations and equations with the $(p,q)$-differential operator and with the generalized $p$-mean curvature operator. Using variational methods, together with truncation and comparison techniques and Morse theory, we prove multiplicity theorems, producing three, five or six nontrivial smooth solutions, all with sign information.