Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations

Jaeyoung Byeon, Ohsang Kwon, Yoshihito Oshita

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    Abstract

    For k = 1, · · ·, K, let Mk be a qk-dimensional smooth compact framed manifold in ℝN with qk ∈ {1, · · ·, N - 1}. We consider the equation -ε2Δu + V(x)u - up = 0 in ℝN where for each k ∈ {1, · · ·, K} and some mk > 0, V(x) = |dist(x, Mk)|mk + O(|dist(x, Mk)|mk+1) as dist(x, Mk) → 0. For a sequence of ε converging to zero, we will find a positive solution uε of the equation which concentrates on M1 ∪ · · · ∪ MK.

    Original languageEnglish
    Pages (from-to)825-842
    Number of pages18
    JournalCommunications on Pure and Applied Analysis
    Volume14
    Issue number3
    DOIs
    Publication statusPublished - May 1 2015

    Keywords

    • Concentration phenomena
    • Infinite dimensional reduction
    • Nondegeneracy
    • Nonlinear schrdinger equation

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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