Ground states of nonlinear Choquard equations with multi-well potentials

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	Ground states of nonlinear Choquard equations with multi-well potentials
	Li, Shuai 1; Xiang, Jianlin 2; Zeng, Xiaoyu 2
刊名	JOURNAL OF MATHEMATICAL PHYSICS
	2016-08-01
卷号	57 期号:8
英文摘要	In this paper, we study minimizers of the Hartree-type energy functional E-a(u) := integral N-R(vertical bar Delta u(x)vertical bar(2) + V(x)vertical bar u(x)vertical bar(2))dx - a/p integral N-R(I-alphavertical bar u(x)vertical bar(p)vertical bar u(x)vertical bar(p))dx, a >= 0 under the mass constraint integral N-R(vertical bar u vertical bar(2)dx = 1, where p = N+alpha+2/N with alpha is an element of (0, N) for N >= 2 is the mass critical exponent. Here I-alpha denotes the Riesz potential and the trapping potential 0 <= V(x) is an element of L-loc(infinity)(R-N) satisfies lim(vertical bar x vertical bar ->infinity) V(x) = infinity . We prove that minimizers exist if and only if a satisfies a < a = parallel to Q parallel to(2(p-1))(2) , where Q is a positive radially symmetric ground state of -Delta u + u = (I-alpha vertical bar u vertical bar(p))vertical bar u vertical bar(p-2)u in R-N. The uniqueness of positive minimizers holds if a > 0 is small enough. The blow-up behavior of positive minimizers as a NE arrow a is also derived under some general potentials. Especially, we prove that minimizers must blow up at the central point of the biggest inscribed sphere of the set Omega := {x is an element of R-N, V(x) = 0} if vertical bar Omega vertical bar > 0. Published by AIP Publishing.
WOS标题词	Science & Technology ; Physical Sciences
类目[WOS]	Physics, Mathematical
研究领域[WOS]	Physics
关键词[WOS]	ELLIPTIC PROBLEMS ; EXISTENCE ; UNIQUENESS ; SYMMETRY
收录类别	SCI
语种	英语
WOS记录号	WOS:000383917300015
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/9593]
专题	武汉物理与数学研究所_数学物理与应用研究部
作者单位	1.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China 2.Wuhan Univ Technol, Sch Sci, Dept Math, Wuhan 430070, Peoples R China
推荐引用方式 GB/T 7714	Li, Shuai,Xiang, Jianlin,Zeng, Xiaoyu. Ground states of nonlinear Choquard equations with multi-well potentials[J]. JOURNAL OF MATHEMATICAL PHYSICS,2016,57(8).
APA	Li, Shuai,Xiang, Jianlin,&Zeng, Xiaoyu.(2016).Ground states of nonlinear Choquard equations with multi-well potentials.JOURNAL OF MATHEMATICAL PHYSICS,57(8).
MLA	Li, Shuai,et al."Ground states of nonlinear Choquard equations with multi-well potentials".JOURNAL OF MATHEMATICAL PHYSICS 57.8(2016).