Standing waves for nonlinear Schrodinger equations with a general nonlinearity: One and two dimensional cases

被引：49

作者：

Byeon, Jaeyoung ^{[1
]}

Jeanjean, Louis ^{[2
]}

Tanaka, Kazunaga ^{[3
]}

机构：

[1] Pohang Univ Sci & Technol, Dept Math, Pohang 790784, Kyungbuk, South Korea

[2] Univ Franche Comte, CNRS, Equipe Math, UMR 6623, F-25030 Besancon, France

[3] Waseda Univ, Sch Sci & Engn, Dept Math, Tokyo 169, Japan

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2008年 / 33卷 / 06期

基金：

新加坡国家研究基金会; 日本学术振兴会;

关键词：

Berestycki-Lions conditions; nonlinear Schrodinger equations; standing waves; variational methods;

D O I：

10.1080/03605300701518174

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For N=1,2, we consider singularly perturbed elliptic equations epsilon(2) Delta u-V(x) u+f(u)=0, u(x)> 0 on R-N, lim(vertical bar x vertical bar ->infinity) u(x)=0. For small epsilon > 0, we show the existence of a localized bound state solution concentrating at an isolated component of positive local minimum of V under conditions on f we believe to be almost optimal; when N >= 3, it was shown in Byeon and Jeanjean (2007).

引用

页码：1113 / 1136

页数：24

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