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

共 50 条

[1] The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory
Chae, D
Imanuvilov, OY
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 215 (01) : 119 - 142
[2] Self-dual radial non-topological solutions to a competitive Chern-Simons model
Chen, Zhijie
Lin, Chang-Shou
ADVANCES IN MATHEMATICS, 2018, 331 : 484 - 541
[3] Non-topological solutions in the generalized self-dual Chern-Simons-Higgs theory
Dongho Chae
Oleg Y. Imanuvilov
Calculus of Variations and Partial Differential Equations, 2003, 16 : 47 - 61
[4] Non-topological solutions in the generalized self-dual Chern-Simons-Higgs theory
Chae, D
Imanuvilov, OY
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2003, 16 (01) : 47 - 61
[5] The Existence of Non-Topological Multivortex Solutions in the Relativistic Self-Dual Chern–Simons Theory
Dongho Chae
Oleg Yu. Imanuvilov
Communications in Mathematical Physics, 2000, 215 : 119 - 142
[6] Non-topological multivortex solutions to the self-dual Maxwell-Chern-Simons-Higgs systems
Chae, D
Imanuvilov, OY
JOURNAL OF FUNCTIONAL ANALYSIS, 2002, 196 (01) : 87 - 118
[7] TOPOLOGICAL SOLUTIONS IN THE SELF-DUAL CHERN-SIMONS THEORY - EXISTENCE AND APPROXIMATION
SPRUCK, J
YANG, YS
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1995, 12 (01): : 75 - 97
[8] On non-topological multivortex condensates in the generalized self-dual Chern-Simons theory
Suzuki, T
Takahashi, F
Recent Advances in Elliptic and Parabolic Problems, 2005, : 259 - 270
[9] Non-topological solutions of the relativistic SU(3) Chern-Simons Higgs model
Wang, GF
Zhang, LQ
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 202 (03) : 501 - 515
[10] Non-topological multi-vortex solutions to the self-dual Chern-Simons-Higgs equation
Chan, H
Fu, CC
Lin, CS
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2002, 231 (02) : 189 - 221

← 1 2 3 4 5 →