| Project/Area Number |
24740100
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | The University of Tokyo (2013-2014)
Keio University (2012) |
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Principal Investigator |
MIYAMOTO Yasuhito 東京大学, 数理(科)学研究科(研究院), 准教授 (90374743)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 優臨界 / 分岐理論 / 非線形楕円型方程式 / 非線形解析 / ノイマン問題 / ディリクレ問題 / Joseph-Lundgren指数 / 大域的分岐構造 / 解構造の分類 / 不完全分岐 / 臨界Sobolev指数 / ソボレフ優臨界 / 楕円型偏微分方程式 / 分岐図式 / Dirichlet問題 / 特異解 |
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| Outline of Final Research Achievements |
I studied the structure of the positive solutions of nonlinear elliptic PDEs. In particular, I studied bifurcation diagrams. Mainly, two results were obtained. I proved that the imperfect bifurcation occurs in the bifurcation diagram of the positive solutions of the Gel'fand problem when the domain is perturbed. I almost completely classified the bifurcation diagrams of the positive radial solutions of the Dirichlet problem of supercritical elliptic PDEs in a ball. I obtained partial results about the bifurcation diagram of the positive radial solutions of the Neumann problem of the supercritical scalar field equation in a ball.
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