Sign-Changing multi-bump solutions for nonlinear schrödinger equations with steep potential wells

Yohei Sato, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    15 Citations (Scopus)

    Abstract

    We study the nonlinear Schrödinger equations: (Pλ) -Δu+(λ2a(x)+1)u = |u|p-1u, u ε H 1(RN), where p > 1 is a subcritical exponent, a(x) is a continuous function satisfying a(x) ≥ 0, 0 < lim inf |x|-∞ a(x) ≤ lim sup|x|-∞ a(x) < ∞ and a-1(0) consists of 2 connected bounded smooth components Ω1 and Ω2. We study the existence of solutions (uλ) of (Pλ) which converge to 0 in RN \ (Ω1Ω 2) and to a prescribed pair (v1(x), v2(x)) of solutions of the limit problem: -Δvi + vi = |v i|p-1vi in Ωi (i = 1, 2) as λ → ∞.

    Original languageEnglish
    Pages (from-to)6205-6253
    Number of pages49
    JournalTransactions of the American Mathematical Society
    Volume361
    Issue number12
    DOIs
    Publication statusPublished - 2009 Dec

    Fingerprint

    Multibump Solutions
    Potential Well
    Nonlinear equations
    Existence of Solutions
    Continuous Function
    Nonlinear Equations
    Exponent
    Converge

    Keywords

    • Critical frequency
    • Nonlinear schrödinger equations
    • Sign-changing solutions
    • Singular perturbation

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    Sign-Changing multi-bump solutions for nonlinear schrödinger equations with steep potential wells. / Sato, Yohei; Tanaka, Kazunaga.

    In: Transactions of the American Mathematical Society, Vol. 361, No. 12, 12.2009, p. 6205-6253.

    Research output: Contribution to journalArticle

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