Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations

Silvia Cingolani, Louis Jeanjean, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    We study, in the semiclassical limit, the singularly perturbed nonlinear Schrödinger equations (Formula presented.)where (Formula presented.), (Formula presented.) is the Schrödinger operator with a magnetic field having source in a (Formula presented.) vector potential A and a scalar continuous (electric) potential V defined by (Formula presented.)Here, 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.) geometrically distinct, complex-valued solutions to (0.1) whose moduli concentrate around K as (Formula presented.).

    Original languageEnglish
    Pages (from-to)1-30
    Number of pages30
    JournalJournal of Fixed Point Theory and Applications
    DOIs
    Publication statusAccepted/In press - 2016 Nov 14

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    Keywords

    • Complex-valued solutions
    • Cuplength
    • Magnetic fields
    • Nonlinear Schrödinger equations
    • Semiclassical limit

    ASJC Scopus subject areas

    • Modelling and Simulation
    • Geometry and Topology
    • Applied Mathematics

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