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arXiv · 1202.0576

Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian

Serena Dipierro·Giampiero Palatucci·Enrico Valdinoci
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Abstract

This paper deals with the following class of nonlocal Schrödinger equations $$ \displaystyle (-Δ)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.

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Serena Dipierro, Giampiero Palatucci, Enrico Valdinoci. 2012-02-02. Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian. https://arxiv.org/abs/1202.0576

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