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

TitleExistence and symmetry results for a Schrodinger type problem involving the fractional Laplacian
Publication TypeJournal Article
Year of Publication2013
AuthorsDipierro, S, Palatucci, G, Valdinoci, E
JournalLe Matematiche (Catania), Vol. 68 (2013), no. 1: 201-216
Abstract

This paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ 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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