TITLE

# Standing waves with a critical frequency for nonlinear Schrï¿½dinger equations, II

AUTHOR(S)
Jaeyoung Byeon; Zhi-Qiang Wang
PUB. DATE
October 2003
SOURCE
Calculus of Variations & Partial Differential Equations;Oct2003, Vol. 18 Issue 2, p207
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
For elliptic equations of the form $\Delta u -V(\varepsilon x) u + f(u)=0, x\in {\bf R}^N$ , where the potential V satisfies $\liminf_{\vert x\vert\to \infty} V(x) > \inf_{{\bf R}^N} V(x) =0$ , we develop a new variational approach to construct localized bound state solutions concentrating at an isolated component of the local minimum of V where the minimum value of V can be positive or zero. These solutions give rise to standing wave solutions having a critical frequency for the corresponding nonlinear Schrï¿½dinger equations. Our method allows a fairly general class of nonlinearity f( u) including ones without any growth restrictions at large.
ACCESSION #
11090216

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