Existence of self-dual non-topological solutions in the Chern-Simons Higgs model

被引：40

作者：

Choe, Kwangseok ^{[2
]}

Kim, Namkwon ^{[1
]}

Lin, Chang-Shou ^{[1
,3
]}

机构：

[1] Chosun Univ, Dept Math, Kwangju 501759, South Korea

[2] Inha Univ, Dept Math, Inchon 402751, South Korea

[3] Natl Taiwan Univ, TIMS, Dept Math, Taipei, Taiwan

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2011年 / 28卷 / 06期

基金：

新加坡国家研究基金会;

关键词：

Semi-linear PDE; Non-topological vortices; Chern-Simons Higgs model; MEAN-FIELD EQUATIONS; BLOW-UP SOLUTIONS; MULTIVORTEX SOLUTIONS;

D O I：

10.1016/j.anihpc.2011.06.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate the existence of non-topological solutions of the Chern-Simons Higgs model in R-2. A long standing problem for this equation is: Given N vortex points and beta > 8 pi (N + 1). does there exist a non-topological solution in R-2 such that the total magnetic flux is equal to beta/2? In this paper, we prove the existence of such a solution if beta is not an element of {8 pi N k/k-1 vertical bar k = 2, ....N}). We apply the bubbling analysis and the Leray-Schauder degree theory to solve this problem. (C) 2011 Elsevier Masson SAS. All rights reserved.

引用

页码：837 / 852

页数：16

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