Subcritical perturbations of resonant linear problems with sign-changing potential

Abstract

We establish existence and multiplicity theorems for a Dirichlet boundary-value problem at resonance. This problem is a nonlinear subcritical perturbation of a linear eigenvalue problem studied by Cuesta, and includes a sign-changing potential. We obtain solutions using the Mountain Pass lemma and the Saddle Point theorem. Our paper extends some recent results of Goncalves, Miyagaki, and Ma.