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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 $s>0$.

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