Limit Configurations of Schrodinger Systems Versus Optimal Partition for the Principal Eigenvalue of Elliptic Systems

doi:10.1515/ans-2019-2057

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	Limit Configurations of Schrodinger Systems Versus Optimal Partition for the Principal Eigenvalue of Elliptic Systems
	Luo, Haijun 3; Zhang, Zhitao 1,2
	2019-11-01
发表期刊	ADVANCED NONLINEAR STUDIES
ISSN	1536-1365
卷号	19 期号:4 页码:693-715
摘要	We study a Schrodinger system of four equations with linear coupling functions and nonlinear couplings, including the case that the corresponding elliptic operators are indefinite. For any given nonlinear coupling beta > 0, we first use minimizing sequences on a normalized set to obtain a minimizer, which implies the existence of positive solutions for some linear coupling constants mu(beta),nu(beta) by Lagrange multiplier rules. Then, as beta -> infinity, we prove that the limit configurations to the competing system are segregated in two groups, develop a variant of Almgren's monotonicity formula to reveal the Lipschitz continuity of the limit profiles and establish a kind of local Pohozaev identity to obtain the extremality conditions. Finally, we study the relation between the limit profiles and the optimal partition for principal eigenvalue of the elliptic system and obtain an optimal partition for principal eigenvalues of elliptic systems.
关键词	Schrodinger System Almgren's Monotonicity Formula Optimal Partition Free Boundary Problem
DOI	10.1515/ans-2019-2057
收录类别	SCI
语种	英语
资助项目	Fundamental Research Funds for the Central Universities[531118010205] ; National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[11688101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000494831500003
出版者	WALTER DE GRUYTER GMBH
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50646
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Zhitao
作者单位	1.Acad Math & Syst Sci, Chinese Acad Sci, HLM, Beijing 100190, Peoples R China 2.Univ Chinese, Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China
推荐引用方式 GB/T 7714	Luo, Haijun,Zhang, Zhitao. Limit Configurations of Schrodinger Systems Versus Optimal Partition for the Principal Eigenvalue of Elliptic Systems[J]. ADVANCED NONLINEAR STUDIES,2019,19(4):693-715.
APA	Luo, Haijun,&Zhang, Zhitao.(2019).Limit Configurations of Schrodinger Systems Versus Optimal Partition for the Principal Eigenvalue of Elliptic Systems.ADVANCED NONLINEAR STUDIES,19(4),693-715.
MLA	Luo, Haijun,et al."Limit Configurations of Schrodinger Systems Versus Optimal Partition for the Principal Eigenvalue of Elliptic Systems".ADVANCED NONLINEAR STUDIES 19.4(2019):693-715.