Stability of standing waves for nonlinear schrödinger equations with critical power nonlinearity and potentials

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Abstract

We study the stability of standing waves eiωtφω(x) for a nonlinear Schrödinger equation with critical power nonlinearity |u|4/nu and a potential V (x) in Rn. Here, ω ∈ R and φω(x) is a ground state of the stationary problem. Under suitable assumptions on V (x), we show that eiωtφω(x) is stable for sufficiently large ω. This result gives a different phenomenon from the case V (x) = 0 where the strong instability was proved by M. I. Weinstein [25].

Original languageEnglish
Pages (from-to)259-276
Number of pages18
JournalAdvances in Differential Equations
Volume10
Issue number3
Publication statusPublished - 2005 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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