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

Serena Dipierro, Giampiero Palatucci, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

Abstract

This paper deals with the following class of nonlocal Schrödinger equations

(-\Delta)^s u + u = |u|^{p-1}u in \mathbb{R}^N, 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.
Original languageEnglish
Pages (from-to)201-216
JournalLe Matematiche: journal of pure and applied mathematics
Volume68
Issue number1
DOIs
Publication statusPublished - 7 May 2013
Externally publishedYes

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