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Existence of solutions for a class of fractional elliptic problems on exterior domains (1812.04878v1)

Published 12 Dec 2018 in math.AP

Abstract: This work concerns with the existence of solutions for the following class of nonlocal elliptic problems \begin{equation*}\label{00} \left{ \begin{array}{l} (-\Delta){s}u + u = |u|{p-2}u\;\;\mbox{in $\Omega$},\ u \geq 0 \quad \mbox{in} \quad \Omega \quad \mbox{and} \quad u \not\equiv 0, \ u=0 \quad \mathbb{R}N \setminus \Omega, \end{array} \right. \end{equation*} involving the fractional Laplacian operator $(-\Delta){s}$, where $s\in (0,1)$, $N> 2s$, $\Omega \subset \RN$ is an exterior domain with (non-empty) smooth boundary $\partial \Omega$ and $p\in (2, 2_{s}{*})$. The main technical approach is based on variational and topological methods. The variational analysis that we perform in this paper dealing with exterior domains is quite general and may be suitable for other goals too.

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