Limit behavior of mass critical Hartree minimization problems with steep potential wells
文献类型：期刊论文
| 作者 | Guo, Yujin4; Luo, Yong3,4; Wang, Zhi-Qiang1,2 |
| 刊名 | JOURNAL OF MATHEMATICAL PHYSICS
 |
| 出版日期 | 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. |
| WOS关键词 | CONCENTRATION-COMPACTNESS PRINCIPLE ; NONLINEAR SCHRODINGER-EQUATIONS ; ATTRACTIVE INTERACTIONS ; STANDING WAVES ; UNIQUENESS ; EXISTENCE ; CALCULUS ; STATES |
| 资助项目 | NSFC[11671394] ; NSFC[11771324] ; MOST[2017YFA0304500] |
| WOS研究方向 | Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000437094100004 |
| 出版者 | AMER INST PHYSICS |
| 资助机构 | NSFC ; NSFC ; MOST ; MOST ; NSFC ; NSFC ; MOST ; MOST ; NSFC ; NSFC ; MOST ; MOST ; NSFC ; NSFC ; MOST ; MOST |
| 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. |
入库方式： OAI收割
来源：武汉物理与数学研究所
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