Elliptic problems on $\mathbbR^N$ with jumping nonlinearities: perturbation results

Abstract

In this paper we study a class of nonlinear elliptic problems in $\mathbb R^N$, where the nonlinearity is of "jumping" type. The problems we study are perturbations of a linear problem at resonance. We use a perturbative method recently developed, and we get results which generalize to the case of an unbounded domain some of the theorems previously known for bounded domains.