Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations

Jaeyoung Byeon, Ohsang Kwon, Yoshihito Oshita

Research output: Contribution to journalArticle

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)|m k + O(|dist(x, Mk)|m k+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

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Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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