Resonant-Superlinear Nonhomogeneous Dirichlet Problems

Abstract

We consider a Dirichlet nonlinear equation driven by the (p, 2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation. We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions all with sign information.