Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations

Jaeyoung Byeon, Ohsang Kwon, Yoshihito Oshita

Research output: Contribution to journal › Article

1 Citation (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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Standing Wave
Nonlinear equations
Compact Manifold
Nonlinear Equations
Smooth Manifold
Positive Solution
Zero

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations. / Byeon, Jaeyoung; Kwon, Ohsang; Oshita, Yoshihito.

In: Communications on Pure and Applied Analysis, Vol. 14, No. 3, 01.05.2015, p. 825-842.

Research output: Contribution to journal › Article

Byeon, J, Kwon, O & Oshita, Y 2015, 'Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations', Communications on Pure and Applied Analysis, vol. 14, no. 3, pp. 825-842. https://doi.org/10.3934/cpaa.2015.14.825
Byeon J, Kwon O, Oshita Y. Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations. Communications on Pure and Applied Analysis. 2015 May 1;14(3):825-842. https://doi.org/10.3934/cpaa.2015.14.825
Byeon, Jaeyoung ; Kwon, Ohsang ; Oshita, Yoshihito. / Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations. In: Communications on Pure and Applied Analysis. 2015 ; Vol. 14, No. 3. pp. 825-842.
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