On spikes concentrating on line-segments to a semilinear Neumann problem

被引：19

作者：

Ao, Weiwei ^{[1
]}

Musso, Monica ^{[2
]}

Wei, Juncheng ^{[1
]}

机构：

[1] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

[2] Pontificia Univ Catolica Chile, Dept Matemat, Macul, Chile

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年 / 251卷 / 4-5期

关键词：

INTERIOR PEAK SOLUTIONS; MULTIPEAK SOLUTIONS; LAYER SOLUTIONS; EXISTENCE; EQUILIBRIA; EQUATION; ENERGY;

D O I：

10.1016/j.jde.2011.05.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the following singularly perturbed Neumann problem -epsilon(2)Delta u + u - u(p) = 0 in Omega, u > 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where p is subcritical and Omega is a smooth and bounded domain in R-n. We construct a new class of solutions which consist of large number of spikes concentrating on an interior straight-line intersecting with partial derivative Omega orthogonally. Our results show that higher-dimensional concentration can exist without resonance condition. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：881 / 901

页数：21

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