A complete classification of ground-states for a coupled nonlinear Schrödinger system
An isomorphism theorem for parabolic problems in Hörmander spaces and its applications
January 2017, 16(1): 99-114. doi: 10.3934/cpaa.2017004
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
Received November 2015 Revised July 2016 Published November 2016
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.
Keywords: Fractional p-Laplacian, superlinear problems, fractional Sobolev space, Cerami condition.
Mathematics Subject Classification: Primary: 35J35, 35J60; Secondary: 35R11.
Citation: CÉSAR E. TORRES LEDESMA. Existence and symmetry result for fractional p-Laplacian in $\mathbb{R}^{n}$. Communications on Pure & Applied Analysis, 2017, 16 (1) : 99-114. doi: 10.3934/cpaa.2017004
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