Normalized solutions of mass subcritical Schrodinger equations in exterior domains
文献类型：期刊论文
| 作者 | Zhang, Zexin2,3; Zhang, Zhitao1,2,3 |
| 刊名 | NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
 |
| 出版日期 | 2022-05-01 |
| 卷号 | 29期号:3页码:25 |
| ISSN号 | 1021-9722 |
| 关键词 | Normalized solution Critical point Minimax theorem Schrodinger equation Exterior domain |
| DOI | 10.1007/s00030-022-00764-5 |
| 英文摘要 | 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. |
| 资助项目 | 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研究方向 | Mathematics |
| 语种 | 英语 |
| 出版者 | SPRINGER INT PUBL AG |
| WOS记录号 | WOS:000777399600001 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60209]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Zhang, Zexin |
| 作者单位 | 1.Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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