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SYMMETRY AND ASYMPTOTIC BEHAVIOR OF GROUND STATE SOLUTIONS FOR SCHRODINGER SYSTEMS WITH LINEAR INTERACTION
Zhang, Zhitao1; Luo, Haijun
2018-05-01
Source PublicationCOMMUNICATIONS ON PURE AND APPLIED ANALYSIS
ISSN1534-0392
Volume17Issue:3Pages:787-806
AbstractWe 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.
KeywordNonlinear elliptic system ground state solution foliated Schwarz symmetric asymptotic limits
DOI10.3934/cpaa.2018040
Language英语
Funding ProjectNational Natural Science Foundation of China[11325107] ; National Natural Science Foundation of China[11331010] ; National Natural Science Foundation of China[11771428]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000439236400003
PublisherAMER INST MATHEMATICAL SCIENCES-AIMS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30792
Collection数学所
Affiliation1.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
Recommended Citation
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.
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