On the number of positive solutions of singularly perturbed ID nonlinear Schrödinger equations

Patricio Felmer, Salomé Martínez, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    We study singularly perturbed ID nonlinear Schrödinger equations (1.1). When V(x) has multiple critical points, (1.1) has a wide variety of positive solutions for small ε and the number of positive solutions increases to ∞ as ε → 0. We give an estimate of the number of positive solutions whose growth order depends on the number of local maxima of V(x). Envelope functions or equivalently adiabatic profiles of high frequency solutions play an important role in the proof.

    Original languageEnglish
    Pages (from-to)253-268
    Number of pages16
    JournalJournal of the European Mathematical Society
    Volume8
    Issue number2
    Publication statusPublished - 2006

    Fingerprint

    Singularly Perturbed
    Nonlinear equations
    Positive Solution
    Nonlinear Equations
    Envelope
    Critical point
    Estimate

    Keywords

    • Adiabatic profiles
    • Nonlinear Schrödinger equations
    • Singular perturbations

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    On the number of positive solutions of singularly perturbed ID nonlinear Schrödinger equations. / Felmer, Patricio; Martínez, Salomé; Tanaka, Kazunaga.

    In: Journal of the European Mathematical Society, Vol. 8, No. 2, 2006, p. 253-268.

    Research output: Contribution to journalArticle

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