Multiplicity of solutions for the plasma problem in two dimensions

doi:10.1016/j.aim.2010.05.012

CSpace > 应用数学研究所

	Multiplicity of solutions for the plasma problem in two dimensions
	Cao, Daomin1 ; Peng, Shuangjie 2; Yan, Shusen 3
	2010-12-01
发表期刊	ADVANCES IN MATHEMATICS
ISSN	0001-8708
卷号	225 期号:5 页码:2741-2785
摘要	Let Omega be a bounded domain in R(2), u(+) = u if u >= 0, u(+) = 0 if u < 0, u(-) = u(+) - u. In this paper we study the existence of solutions to the following problem arising in the study of a simple model of a confined plasma (P(lambda)) {Delta u - lambda u(-) = o, in Omega, u = c, on partial derivative Omega, integral partial derivative u/partial derivative nu ds = I, partial derivative Omega where nu is the outward unit normal of partial derivative Omega at x, c is a constant which is unprescribed, and I is a given positive constant. The set Omega(p) = {x is an element of Omega, u(x) < 0} is called plasma set. Existence of solutions whose plasma set consisting of one component and asymptotic behavior of plasma set were studied by Caffarelli and Friedman (1980) [3] for large lambda. Under the condition that the homology of Omega is nontrivial we obtain in this paper by a constructive way that for any given integer k >= 1, there is lambda(k) > 0 such that for lambda > lambda(k), (P(lambda)) has a solution with plasma set consisting of k components. (C) 2010 Elsevier Inc. All rights reserved.
关键词	Semilinear elliptic equations Variational method Multiple solutions Free boundary Asymptotic behavior
DOI	10.1016/j.aim.2010.05.012
语种	英语
资助项目	Natural Science Foundation of China[10631030] ; Natural Science Foundation of China[10721101] ; Program for New Century Excellent Talents in University[07-0350] ; ARC in Australia
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000281888400017
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9744
专题	应用数学研究所
通讯作者	Cao, Daomin
作者单位	1.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China 2.Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China 3.Univ New England, Sch Math Stat & Comp Sci, Armidale, NSW 2351, Australia
推荐引用方式 GB/T 7714	Cao, Daomin,Peng, Shuangjie,Yan, Shusen. Multiplicity of solutions for the plasma problem in two dimensions[J]. ADVANCES IN MATHEMATICS,2010,225(5):2741-2785.
APA	Cao, Daomin,Peng, Shuangjie,&Yan, Shusen.(2010).Multiplicity of solutions for the plasma problem in two dimensions.ADVANCES IN MATHEMATICS,225(5),2741-2785.
MLA	Cao, Daomin,et al."Multiplicity of solutions for the plasma problem in two dimensions".ADVANCES IN MATHEMATICS 225.5(2010):2741-2785.