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

Jaeyoung Byeon; Yoshihito Oshita

doi:10.1081/PDE-200040205

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

Jaeyoung Byeon, Yoshihito Oshita

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

For elliptic equations of the form ε²Δu - V(x)u + u^p = 0, x ∈ R^N, where the potential V satisfies lim inf _|x|→∞ V(x) > inf_RN 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 language	English
Pages (from-to)	1877-1904
Number of pages	28
Journal	Communications in Partial Differential Equations
Volume	29
Issue number	11-12
DOIs	https://doi.org/10.1081/PDE-200040205
Publication status	Published - 2004
Externally published	Yes

Keywords

Critical frequency
Nondegeneracy
Nonlinear Schrodinger equations
Standing waves

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1081/PDE-200040205

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AB - 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.

KW - Critical frequency

KW - Nondegeneracy

KW - Nonlinear Schrodinger equations

KW - Standing waves

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