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

CÉSAR E. TORRES LEDESMA

doi:10.3934/cpaa.2017004

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2017, Volume 16, Issue 1: 99-114. Doi: 10.3934/cpaa.2017004

This issue Previous Article An isomorphism theorem for parabolic problems in Hörmander spaces and its applications Next Article A complete classification of ground-states for a coupled nonlinear Schrödinger system

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

CÉSAR E. TORRES LEDESMA

Departamento de Matemáticas, Universidad Nacional de Trujillo, Av. Juan Pablo Ⅱ s/n, Trujillo, Perú

Author Bio: E-mail address: ctorres@dim.uchile.cl, ctl_576@yahoo.es

Received: November 2015

Revised: July 2016

Published: January 2018

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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.

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Mathematics Subject Classification: Primary: 35J35, 35J60; Secondary: 35R11.

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