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*} &(-Δ)_{p}^αu + V(x)u^{p-2}u = f(x,u) \mbox{ in } \mathbb{R}^{n}, \end{eqnarray*} where $p\ge 2$, $0<s<1$, $n\ge 2$ 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.

References in corpus (2)

• Gamma-convergence of nonlocal perimeter functionals
• Existence results for fractional p-Laplacian problems via Morse theory

Cited by in corpus (1)

• Multiple solutions for a fractional $p$-Laplacian equation with sign-changing potential