Limit behavior of mass critical Hartree minimization problems with steep potential wells

doi:10.1063/1.5025730

	Limit behavior of mass critical Hartree minimization problems with steep potential wells
	Guo, Yujin 4; Luo, Yong 3,4; Wang, Zhi-Qiang 1,2
刊名	JOURNAL OF MATHEMATICAL PHYSICS
	2018-06-01
卷号	59 期号:6 页码:19
ISSN号	0022-2488
DOI	10.1063/1.5025730
英文摘要	We consider minimizers of the following mass critical Hartree minimization problem: e(lambda)(N) := inf({u is an element of H1(Rd), parallel to u parallel to 22=N}) E-lambda(u), where d >= 3, lambda > 0, and the Hartree energy functional E-lambda(u) is defined by E-lambda(u) := integral(Rd) vertical bar del u(x)vertical bar(2)dx + lambda integral(Rd) g(x)u(2)(x)dx - 1/2 integral(Rd) integral(Rd) u(2)(x)u(2)(y)/vertical bar x-y vertical bar(2) dxdy.Here the steep potential g(x) satisfies 0 = g(0) = inf(Rd) g(x) <= g(x) <= 1 and 1 - g(x) is an element of L-2/d(R-d). We prove that there exists a constant N* > 0, independent of lambda g(x), such that if N >= N, then e(lambda)(N) does not admit minimizers for any lambda > 0; if 0 < N < N, then there exists a constant lambda(N) > 0 such that e(lambda)(N) admits minimizers for any lambda > lambda(N) and e(lambda)(N) does not admit minimizers for 0 < lambda < lambda(N). For any given 0 < N < N, the limit behavior of positive minimizers for e(lambda)(N) is also studied as lambda -> infinity, where the mass concentrates at the bottom of g(x). Published by AIP Publishing.
资助项目	NSFC[11671394] ; NSFC[11771324] ; MOST[2017YFA0304500]
WOS关键词	CONCENTRATION-COMPACTNESS PRINCIPLE ; NONLINEAR SCHRODINGER-EQUATIONS ; ATTRACTIVE INTERACTIONS ; STANDING WAVES ; UNIQUENESS ; EXISTENCE ; CALCULUS ; STATES
WOS研究方向	Physics
语种	英语
出版者	AMER INST PHYSICS
WOS记录号	WOS:000437094100004
资助机构	NSFC ; NSFC ; MOST ; MOST ; NSFC ; NSFC ; MOST ; MOST ; NSFC ; NSFC ; MOST ; MOST ; NSFC ; NSFC ; MOST ; MOST
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/21353]
专题	中国科学院武汉物理与数学研究所
通讯作者	Guo, Yujin
作者单位	1.Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA 2.Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100190, Peoples R China 4.Chinese Acad Sci, Wuhan Inst Phys & Math, POB 71010, Wuhan 430071, Hubei, Peoples R China
推荐引用方式 GB/T 7714	Guo, Yujin,Luo, Yong,Wang, Zhi-Qiang. Limit behavior of mass critical Hartree minimization problems with steep potential wells[J]. JOURNAL OF MATHEMATICAL PHYSICS,2018,59(6):19.
APA	Guo, Yujin,Luo, Yong,&Wang, Zhi-Qiang.(2018).Limit behavior of mass critical Hartree minimization problems with steep potential wells.JOURNAL OF MATHEMATICAL PHYSICS,59(6),19.
MLA	Guo, Yujin,et al."Limit behavior of mass critical Hartree minimization problems with steep potential wells".JOURNAL OF MATHEMATICAL PHYSICS 59.6(2018):19.