Standing waves for nonlinear Schrödinger equations with a general nonlinearity: One and two dimensional cases

Jaeyoung Byeon, Louis Jeanjean, Kazunaga Tanaka

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

For N = 1,2, we consider singularly perturbed elliptic equations ε2Δ u - V(x) u + f(u)= 0, u(x)> 0 on RN, lim|x|→∞u(x)= 0. For small ε > 0, we show the existence of a localized bound state solution concentrating at an isolated component of positive local minimum of V under conditions on f we believe to be almost optimal; when N ≥ 3, it was shown in Byeon and Jeanjean (2007).

Original languageEnglish
Pages (from-to)1113-1136
Number of pages24
JournalCommunications in Partial Differential Equations
Volume33
Issue number6
DOIs
Publication statusPublished - 2008 Jun 1

Keywords

  • Berestycki-Lions conditions
  • Nonlinear Schrödinger equations
  • Standing waves
  • Variational methods

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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