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Limit Configurations of Schrodinger Systems Versus Optimal Partition for the Principal Eigenvalue of Elliptic Systems
Luo, Haijun3; Zhang, Zhitao1,2
2019-11-01
Source PublicationADVANCED NONLINEAR STUDIES
ISSN1536-1365
Volume19Issue:4Pages:693-715
AbstractWe 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.
KeywordSchrodinger System Almgren's Monotonicity Formula Optimal Partition Free Boundary Problem
DOI10.1515/ans-2019-2057
Indexed BySCI
Language英语
Funding ProjectFundamental Research Funds for the Central Universities[531118010205] ; National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[11688101]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000494831500003
PublisherWALTER DE GRUYTER GMBH
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50646
Collection中国科学院数学与系统科学研究院
Corresponding AuthorZhang, Zhitao
Affiliation1.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
Recommended Citation
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.
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