Uniqueness of ground states for nonlinear Hartree equations

doi:10.1063/1.5051026

	Uniqueness of ground states for nonlinear Hartree equations
	Luo, Yong 1,2
刊名	JOURNAL OF MATHEMATICAL PHYSICS
	2018-08-01
卷号	59 期号:8 页码:18
ISSN号	0022-2488
DOI	10.1063/1.5051026
英文摘要	We consider ground states of nonlinear Hartree equations with trapping potentials V(x), which can be described equivalently by positive minimizers of L-2-critical Hartree energy functional. It is known that ground states exist if and only if the parameter a satisfies a < a:= parallel to Q parallel to(2)(2), where Q is the unique ground state of Delta Q-Q+ (integral(R4) Q(2)(y)/vertical bar x-y vertical bar(2)dy) Q = 0 in R-4. In this paper, we prove the uniqueness of ground states as a NE arrow a, where the potential V(x) = p(x) h(x), 0 < C <= p(x) <= 1/C, h(x) is homogeneous of degree q >= 2, and however H(y) = integral(R4) h(x + y) Q(2)(x)dx admits a unique and non-degenerate critical point. Published by AIP Publishing.
资助项目	NSFC[11671394]
WOS关键词	SCHRODINGER-EQUATION ; POTENTIALS ; EXISTENCE ; SYMMETRY
WOS研究方向	Physics
语种	英语
出版者	AMER INST PHYSICS
WOS记录号	WOS:000443724800008
资助机构	NSFC ; NSFC ; NSFC ; NSFC ; NSFC ; NSFC ; NSFC ; NSFC
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/13086]
专题	中国科学院武汉物理与数学研究所
通讯作者	Luo, Yong
作者单位	1.Univ Chinese Acad Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Hubei, Peoples R China
推荐引用方式 GB/T 7714	Luo, Yong. Uniqueness of ground states for nonlinear Hartree equations[J]. JOURNAL OF MATHEMATICAL PHYSICS,2018,59(8):18.
APA	Luo, Yong.(2018).Uniqueness of ground states for nonlinear Hartree equations.JOURNAL OF MATHEMATICAL PHYSICS,59(8),18.
MLA	Luo, Yong."Uniqueness of ground states for nonlinear Hartree equations".JOURNAL OF MATHEMATICAL PHYSICS 59.8(2018):18.