Existence of solution for a class of problem in whole ${\mathbb{R}}^N$ without the Ambrosetti-Rabinowitz condition

Abstract

In this paper we study the existence of solution for a class of elliptic problem in whole ${\mathbb{R}}^N$ without the well known Ambrosetti-Rabinowitz condition. Here, we do not assume any monotonicity condition on $f(s)/s$ for $s>0$.