-Laplacian in $\mathbb{R}^{n}$ Article Swipe

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Fractional Laplacian Mountain pass theorem Combinatorics Physics Mathematical physics Laplace operator Symmetry (geometry) Mathematics Mathematical analysis Quantum mechanics Geometry Nonlinear system

César E. Torres Ledesma ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.3934/cpaa.2017004 · OA: W2553956113

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.