KMS Of Academy of mathematics and systems sciences, CAS
Normalized solutions of mass subcritical Schrodinger equations in exterior domains | |
Zhang, Zexin1,2; Zhang, Zhitao1,2,3 | |
2022-05-01 | |
Source Publication | NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS |
ISSN | 1021-9722 |
Volume | 29Issue:3Pages:25 |
Abstract | In this paper, we study the nonlinear Schrodinger equation with L-2-norm constraint: {-Delta u = lambda u + vertical bar u vertical bar(p-2) u in Omega, u = 0 on partial derivative Omega, integral(Omega) vertical bar u vertical bar(2) dx = a(2), where N >= 3, Omega subset of R-N is an exterior domain, i.e., Omega is an unbounded domain with R-N\(Omega) over bar non-empty and bounded, a > 0, 2 < p < 2 + 4/N, and lambda is an element of R is Lagrange multiplier, which appears due to the mass constraint parallel to u parallel to(L2(Omega)) = a. We use Brouwer degree, barycentric functions and minimax method to prove that for any a > 0, there is a positive solution u is an element of H-0(1)(Omega) for some lambda < 0 if R-N\Omega is contained in a small ball. In addition, if we remove the restriction on Omega but impose that a > 0 is small, then we also obtain a positive solution u is an element of H-0(1)(Omega) for some lambda < 0. If Omega is the complement of unit ball in R-N, then for any a > 0, we get a positive radial solution u is an element of H-0(1) (Omega) for some lambda < 0 by Ekeland variational principle. Moreover, we use genus theory to obtain infinitely many radial solutions {(u(n), lambda(n))} with lambda(n) < 0, I-p(u(n)) < 0 for n >= 1 and I-p(u(n)) -> 0(-) as n -> infinity, where I-p is the corresponding energy functional. |
Keyword | Normalized solution Critical point Minimax theorem Schrodinger equation Exterior domain |
DOI | 10.1007/s00030-022-00764-5 |
Indexed By | SCI |
Language | 英语 |
Funding Project | National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[12031015] ; National Natural Science Foundation of China[12026217] ; National Natural Science Foundation of China[11871302] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000777399600001 |
Publisher | SPRINGER INT PUBL AG |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60210 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Zhang, Zexin |
Affiliation | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China 3.Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Peoples R China |
Recommended Citation GB/T 7714 | Zhang, Zexin,Zhang, Zhitao. Normalized solutions of mass subcritical Schrodinger equations in exterior domains[J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS,2022,29(3):25. |
APA | Zhang, Zexin,&Zhang, Zhitao.(2022).Normalized solutions of mass subcritical Schrodinger equations in exterior domains.NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS,29(3),25. |
MLA | Zhang, Zexin,et al."Normalized solutions of mass subcritical Schrodinger equations in exterior domains".NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS 29.3(2022):25. |
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