Existence and symmetry result for Fractional p-Laplacian in $\mathbb{R}^{n}$

Abstract

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