2011 Fiscal Year Final Research Report
A comprehensive study of nonlinear problems via variational approaches
| Project/Area Number |
20340037
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Waseda University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
OZAWA Tohru 早稲田大学, 理工学術院, 教授 (70204196)
OTANI Mitsuharu 早稲田大学, 理工学術院, 教授 (30119656)
NISHIDA Takaaki 早稲田大学, 理工学術院, 教授 (70026110)
YAMAZAKI Masao 早稲田大学, 理工学術院, 教授 (20174659)
YAMADA Yoshio 早稲田大学, 理工学術院, 教授 (20111825)
YANAGIDA Eiji 東京工業大学, 理工学研究科, 教授 (80174548)
KURATA Kazuhiro 首都大学東京, 理工学研究科, 教授 (10186489)
ADACHI Shinji 静岡大学, 工学部, 准教授 (40339685)
HIRATA Jun 早稲田大学, 理工学術院, 助手 (10580483)
SEKIGUCHI Masayoshi 木更津工業高等専門学校, 基礎学系, 教授 (30236088)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 変分問題 / 非線型楕円型方程式 / 特異摂動問題 / ハミルトン系 |
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| Research Abstract |
We study nonlinear problems via variational approaches. Especially (1) we study singular perturbation problems for nonlinear Schrodinger equations and systems. We introduce a new purely variational method which enables us to construct concentrating solutions in a very general setting. (2) We study nonlinear elliptic equations and systems in various settings. We give a new variational construction of radially symmetric ground states. We also study stability and instability of solutions. (3) We also study highly oscillatory solutions in 1-dimensional singular perturbation problems. We give characterization and existence result.
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Research Products
(49 results)
