| Project/Area Number |
20540216
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Osaka City University |
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Principal Investigator |
TAKAHASHI Futoshi Osaka City University, 大学院・理学研究科, 教授 (10374901)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIO Masaharu 大阪市立大学, 大学院・理学研究科, 准教授 (90228156)
ATO Shin 大阪市立大学, 大学院・理学研究科, 准教授 (10243354)
SATO Tomohiko 学習院大学, 理学部, 客員研究員 (50397676)
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| Co-Investigator(Renkei-kenkyūsha) |
UZUKI Takashi 大阪大学, ・基礎工学研究科, 教授 (40114516)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 臨界型変分問題 / 爆発解析 / 解の定性的性質 / 漸近的非退化性 / 漸近的一意性 / 臨界ソボレフ指数 / 多重爆発解 / 臨界Sobolev型方程式 / 漸近解析 / ハミルトニアン / グリーン関数 / 爆発解 / 臨界型方程式 / 非線形楕円型境界値問題 / Robin関数 / 係数関数の影響 |
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| Research Abstract |
In this research, we studied various nonlinear elliptic equations associated with variational problem of so called "critical type". By using the intrinsic scale invariance of the equations involved, we made "blow up analysis" of non-compact solution sequences to the equations and by exploiting the explicit structure of solution set of the limit equations, we obtain various qualitative properties of blowing up solutions, such as asymptotic nondegeneracy, asymptotic uniqueness, and so on. Also we studied spectral property of blowing up solutions and obtain several results on this matter.
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