SYMMETRY AND ASYMPTOTIC BEHAVIOR OF GROUND STATE SOLUTIONS FOR SCHRODINGER SYSTEMS WITH LINEAR INTERACTION

doi:10.3934/cpaa.2018040

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	SYMMETRY AND ASYMPTOTIC BEHAVIOR OF GROUND STATE SOLUTIONS FOR SCHRODINGER SYSTEMS WITH LINEAR INTERACTION
	Zhang, Zhitao1 ; Luo, Haijun
刊名	COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
	2018-05-01
卷号	17 期号:3 页码:787-806
关键词	Nonlinear elliptic system ground state solution foliated Schwarz symmetric asymptotic limits
ISSN号	1534-0392
DOI	10.3934/cpaa.2018040
英文摘要	We study symmetry and asymptotic behavior of ground state solutions for the doubly coupled nonlinear Schrodinger elliptic system { -Delta u + lambda(1)u+ kappa v = mu(1)u(3) + beta uv(2) in Omega, -Delta v + lambda(2)v + kappa u = mu(2)v(3) + beta u(2)v in Omega, u = v = 0 on partial derivative Omega (or u, v is an element of H-1(R-N) as Omega = R-N,R- where N <= 3,Omega subset of R-N is a smooth domain. First we establish the symmetry of ground state solutions, that is, when Omega is radially symmetric, we show that ground state solution is foliated Schwarz symmetric with respect to the same point. Moreover, ground state solutions must be radially symmetric under the condition that Omega is a ball or the whole space R-N. Next we investigate the asymptotic behavior of positive ground state solution as k -> 0(-) , which shows that the limiting profile is exactly a minimizer for c(0) (the minimized energy constrained on Nehari manifold corresponds to the limit systems). Finally for a system with three equations, we prove the existence of ground state solutions whose all components are nonzero.
资助项目	National Natural Science Foundation of China[11325107] ; National Natural Science Foundation of China[11331010] ; National Natural Science Foundation of China[11771428]
WOS研究方向	Mathematics
语种	英语
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
WOS记录号	WOS:000439236400003
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/30791]
专题	数学所
通讯作者	Zhang, Zhitao
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, CEMS, HLM, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Zhitao,Luo, Haijun. SYMMETRY AND ASYMPTOTIC BEHAVIOR OF GROUND STATE SOLUTIONS FOR SCHRODINGER SYSTEMS WITH LINEAR INTERACTION[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2018,17(3):787-806.
APA	Zhang, Zhitao,&Luo, Haijun.(2018).SYMMETRY AND ASYMPTOTIC BEHAVIOR OF GROUND STATE SOLUTIONS FOR SCHRODINGER SYSTEMS WITH LINEAR INTERACTION.COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,17(3),787-806.
MLA	Zhang, Zhitao,et al."SYMMETRY AND ASYMPTOTIC BEHAVIOR OF GROUND STATE SOLUTIONS FOR SCHRODINGER SYSTEMS WITH LINEAR INTERACTION".COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 17.3(2018):787-806.