Limit Configurations of Schrodinger Systems Versus Optimal Partition for the Principal Eigenvalue of Elliptic Systems
文献类型：期刊论文
| 作者 | Luo, Haijun3; Zhang, Zhitao1,2 |
| 刊名 | ADVANCED NONLINEAR STUDIES
 |
| 出版日期 | 2019-11-01 |
| 卷号 | 19期号:4页码:693-715 |
| 关键词 | Schrodinger System Almgren's Monotonicity Formula Optimal Partition Free Boundary Problem |
| ISSN号 | 1536-1365 |
| DOI | 10.1515/ans-2019-2057 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000494831500003 |
| 出版者 | WALTER DE GRUYTER GMBH |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50645]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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