Existence of multi-bump standing waves with a critical frequency for nonlinear Schrödinger equations

Jaeyoung Byeon, Yoshihito Oshita

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

For elliptic equations of the form ε2Δu - V(x)u + up = 0, x ∈ RN, where the potential V satisfies lim inf |x|→∞ V(x) > infRN V(x) = 0, we prove the existence of new kinds of solutions, corresponding to semi-classical standing waves for nonlinear Schrödinger equations, with several local maximum points whose local maximum values are of different scales with respect to ε → 0.

Original languageEnglish
Pages (from-to)1877-1904
Number of pages28
JournalCommunications in Partial Differential Equations
Volume29
Issue number11-12
DOIs
Publication statusPublished - 2004
Externally publishedYes

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Standing Wave
Nonlinear equations
Nonlinear Equations
Elliptic Equations
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Keywords

  • Critical frequency
  • Nondegeneracy
  • Nonlinear Schrodinger equations
  • Standing waves

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics

Cite this

Existence of multi-bump standing waves with a critical frequency for nonlinear Schrödinger equations. / Byeon, Jaeyoung; Oshita, Yoshihito.

In: Communications in Partial Differential Equations, Vol. 29, No. 11-12, 2004, p. 1877-1904.

Research output: Contribution to journalArticle

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