Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities

Louis Jeanjean, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    128 Citations (Scopus)

    Abstract

    We consider a class of equations of the form -ε2 Δu + V (x)u = f(u), u ∈ H1 (RN). By variational methods, we show the existence of families of positive solutions concentrating around local minima of the potential V(x), as ε → 0. We do not require uniqueness of the ground state solutions of the associated autonomous problems nor the monotonicity of the function ξ → f(ξ)/ξ. We deal with asymptotically linear as well as superlinear nonlinearities.

    Original languageEnglish
    Pages (from-to)287-318
    Number of pages32
    JournalCalculus of Variations and Partial Differential Equations
    Volume21
    Issue number3
    DOIs
    Publication statusPublished - 2004 Nov

    Fingerprint

    Ground State Solution
    Asymptotically Linear
    Singularly Perturbed Problem
    Local Minima
    Variational Methods
    Elliptic Problems
    Ground state
    Monotonicity
    Positive Solution
    Uniqueness
    Nonlinearity
    Family
    Form
    Class

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Applied Mathematics

    Cite this

    Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities. / Jeanjean, Louis; Tanaka, Kazunaga.

    In: Calculus of Variations and Partial Differential Equations, Vol. 21, No. 3, 11.2004, p. 287-318.

    Research output: Contribution to journalArticle

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