Existence and symmetry result for fractional <i>p</i>-Laplacian in $\mathbb{R}^{n}$

Abstract

In this article we are interested in the following fractional $p$-Laplacian equation in $\mathbb{R}^n$$(-\Delta)_{p}^{s}u + V(x)|u|^{p-2}u = f(x,u) \mbox{ in } \mathbb{R}^{n},$where $p\geq 2$, $0 < s < 1$, $n\geq 2$ and $f$ is $p$-superlinear. By using mountain pass theorem with Cerami condition we prove the existence of nontrivial solution. Furthermore, we show that this solution is radially simmetry.