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

    34 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

    Fingerprint

    Standing Wave
    Singularly Perturbed
    Bound States
    Local Minima
    Nonlinear equations
    Elliptic Equations
    Nonlinear Equations
    Nonlinearity

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Applied Mathematics

    Cite this

    Standing waves for nonlinear Schrödinger equations with a general nonlinearity : One and two dimensional cases. / Byeon, Jaeyoung; Jeanjean, Louis; Tanaka, Kazunaga.

    In: Communications in Partial Differential Equations, Vol. 33, No. 6, 06.2008, p. 1113-1136.

    Research output: Contribution to journalArticle

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