STANDING WAVE CONCENTRATING ON COMPACT MANIFOLDS FOR NONLINEAR SCHRODINGER EQUATIONS

被引：2

作者：

Byeon, Jaeyoung ^{[1
]}

Kwon, Ohsang ^{[2
]}

Oshita, Yoshihito ^{[3
]}

机构：

[1] Korea Adv Inst Sci & Technol, Dept Math Sci, Taejon 305701, South Korea

[2] Chungbuk Natl Univ, Dept Math, Cheongju 362763, Chungbuk, South Korea

[3] Okayama Univ, Dept Math, Okayama 7008530, Japan

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2015年 / 14卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

Concentration phenomena; infinite dimensional reduction; nondegeneracy; nonlinear Schrdinger equation; POSITIVE BOUND-STATES; MULTI-BUMP SOLUTIONS; CRITICAL FREQUENCY; SEMICLASSICAL STATES; ELLIPTIC-EQUATIONS; RADIAL SOLUTIONS; EXISTENCE; POTENTIALS; SYMMETRY; UNIQUENESS;

D O I：

10.3934/cpaa.2015.14.825

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For k = 1, ... , K, let M-k be a q(k)-dimensional smooth compact framed manifold in R-N with q(k) epsilon {1, ... , N - 1}. We consider the equation -epsilon(2) Delta u + V(x)u - u(p) = 0 in R-N where for each k epsilon {1, ... , K} and some m(k) > 0; V (x) = |dist(x, M-k)|(mk) + O(|dist(x, M-k)|(mk+1)) as dist( x, M-k) -> 0. For a sequence of epsilon converging to zero, we will find a positive solution u(epsilon) of the equation which concentrates on M-1 boolean OR ... boolean OR M-K.

引用

页码：825 / 842

页数：18

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