Multiplicity of positive solutions of nonlinear Schrödinger equations concentrating at a potential well

Silvia Cingolani, Louis Jeanjean, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    We consider singularly perturbed nonlinear Schrödinger equations (Formula Presented) where (Formula Presented) and f is a nonlinear term which satisfies the so-called Berestycki–Lions conditions. We assume that there exists a bounded domain (Formula Presented) such that (Formula Presented) and we set (Formula Presented). For (Formula Presented) small we prove the existence of at least (Formula Presented) solutions to (0.1) concentrating, as (Formula Presented) around K. We remark that, under our assumptions of f, the search of solutions to (0.1) cannot be reduced to the study of the critical points of a functional restricted to a Nehari manifold.

    Original languageEnglish
    Pages (from-to)413-439
    Number of pages27
    JournalCalculus of Variations and Partial Differential Equations
    Volume53
    Issue number1-2
    DOIs
    Publication statusPublished - 2015

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    Potential Well
    Nonlinear equations
    Positive Solution
    Multiplicity
    Nonlinear Equations
    Nehari Manifold
    Singularly Perturbed
    Bounded Domain
    Critical point
    Term

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Multiplicity of positive solutions of nonlinear Schrödinger equations concentrating at a potential well. / Cingolani, Silvia; Jeanjean, Louis; Tanaka, Kazunaga.

    In: Calculus of Variations and Partial Differential Equations, Vol. 53, No. 1-2, 2015, p. 413-439.

    Research output: Contribution to journalArticle

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