Ground states and concentration phenomena for the fractional Schrödinger equation

Mouhamed Moustapha Fall, Fethi Mahmoudi, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

94 Citations (Scopus)

Abstract

We consider here solutions of the nonlinear fractional Schrödinger equation We show that concentration points must be critical points for V. We also prove that if the potential V is coercive and has a unique global minimum, then ground states concentrate suitably at such a minimal point as ε tends to zero. In addition, if the potential V is radial and radially decreasing, then the minimizer is unique provided ε is small.

Original languageEnglish
Pages (from-to)1937-1961
Number of pages25
JournalNonlinearity
Volume28
Issue number6
DOIs
Publication statusPublished - 1 Jun 2015
Externally publishedYes

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