2017 Fiscal Year Final Research Report
Variational study of nonlinear elliptic problems
| Project/Area Number |
25287025
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Waseda University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
小薗 英雄 早稲田大学, 理工学術院, 教授 (00195728)
山田 義雄 早稲田大学, 理工学術院, 教授 (20111825)
大谷 光春 早稲田大学, 理工学術院, 教授 (30119656)
小澤 徹 早稲田大学, 理工学術院, 教授 (70204196)
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| Co-Investigator(Renkei-kenkyūsha) |
ADACHI Shinji 静岡大学, 工学部, 教授 (40339685)
IKOMA Norihisa 金沢大学, 理学部, 准教授 (50728342)
SATO Yohei 埼玉大学, 理工学研究科, 准教授 (00465387)
KURATA Kazuhiro 首都大学東京, 理工学研究科, 教授 (10186489)
Shioji Naoki 横浜国立大学, 工学研究院, 教授 (50215943)
KANEKO Yuki 早稲田大学, 理工学術院, 助教 (40773916)
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| Research Collaborator |
Hirata Jun
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Keywords | 変分問題 / 非線形楕円型方程式 / 特異摂動問題 / ミニマックス法 |
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| Outline of Final Research Achievements |
Via variational approached, we study nonlinear elliptic problems. In particular, we develop a new variational approach and we construct concentrating solutions for several singular perturbation problems, where uniqueness and non-degenerary of solutions of limit problems are not known and the Lyapunov-Schmidt reduction method is not applicable.
We also introduce new variational approaches based on the scaling properties the problems, which enable us to study ground states and other solutions for several nonlinear elliptic equations and systmes.
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| Free Research Field |
解析学
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