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	A Concentration Behavior for Semilinear Elliptic Systems with Indefinite Weight
	Xue Xiu ZHONG ; Wen Ming ZOU ; Xue Xiu ZHONG ; Wen Ming ZOU
	2016-03-30 ; 2016-03-30
关键词	Schrdinger systems concentration ground state solution O175.25
其他题名	A Concentration Behavior for Semilinear Elliptic Systems with Indefinite Weight
中文摘要	Consider the Schrdinger system{-Δu+V1,nu=αQn(x)︱u︱α-2u︱v︱β,-Δv+V2,nv=βQn(x)︱u︱α︱v︱β-2v,u,v∈H10(Ω) where ΩR~N,α,β> 1,α + β< 2* and the spectrum σ(-△ + V_(i,n))(0,+∞),i = 1,2;Q_n is a bounded function and is positive in a region contained in Ω and negative outside.Moreover,the sets{Q_n > 0} shrink to a point x_0∈Ω as n→+∞.We obtain the concentration phenomenon.Precisely,we first show that the system has a nontrivial solution(u_n,v_n) corresponding to Q_n,then we prove that the sequences(u_n) and(v_n) concentrate at x_0 with respect to the H~1-norm.Moreover,if the sets {Q_n > 0} shrink to finite points and(u_n,v_n) is a ground state solution,then we must have that both u_n and v_n concentrate at exactly one of these points.Surprisingly,the concentration of u_n and v_n occurs at the same point.Hence,we generalize the results due to Ackermann and Szulkin.; Consider the Schrdinger system{-Δu+V1,nu=αQn(x)︱u︱α-2u︱v︱β,-Δv+V2,nv=βQn(x)︱u︱α︱v︱β-2v,u,v∈H10(Ω) where ΩR~N,α,β> 1,α + β< 2* and the spectrum σ(-△ + V_(i,n))(0,+∞),i = 1,2;Q_n is a bounded function and is positive in a region contained in Ω and negative outside.Moreover,the sets{Q_n > 0} shrink to a point x_0∈ Ω as n→+∞.We obtain the concentration phenomenon.Precisely,we first show that the system has a nontrivial solution(u_n,v_n) corresponding to Q_n,then we prove that the sequences(u_n) and(v_n) concentrate at x_0 with respect to the H~1-norm.Moreover,if the sets {Q_n > 0} shrink to finite points and(u_n,v_n) is a ground state solution,then we must have that both u_n and v_n concentrate at exactly one of these points.Surprisingly,the concentration of u_n and v_n occurs at the same point.Hence,we generalize the results due to Ackermann and Szulkin.
语种	英语 ; 英语
内容类型	期刊论文
源URL	[http://ir.lib.tsinghua.edu.cn/ir/item.do?handle=123456789/145999]
专题	清华大学
推荐引用方式 GB/T 7714	Xue Xiu ZHONG,Wen Ming ZOU,Xue Xiu ZHONG,et al. A Concentration Behavior for Semilinear Elliptic Systems with Indefinite Weight[J],2016, 2016.
APA	Xue Xiu ZHONG,Wen Ming ZOU,Xue Xiu ZHONG,&Wen Ming ZOU.(2016).A Concentration Behavior for Semilinear Elliptic Systems with Indefinite Weight..
MLA	Xue Xiu ZHONG,et al."A Concentration Behavior for Semilinear Elliptic Systems with Indefinite Weight".(2016).

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