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

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

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


    \begin{equation} \\ \end{equation}
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