Uniqueness and multiplicity of solutions of nonlinear elliptic problems
| Project/Area Number |
26400160
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Yokohama National University |
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Principal Investigator |
SHIOJI Naoki 横浜国立大学, 大学院工学研究院, 教授 (50215943)
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| Research Collaborator |
WATANABE Kohtaro
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 一意性 / 正値球対称解 / 非退化性 / Pohozaev関数 / 分岐 / 弾性曲線 / 楕円型方程式 / 正値解 / 双曲空間 / 分数べきラプラシアン / 臨界べき |
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| Outline of Final Research Achievements |
Using a generalized Pohozaev function, we extend the uniqueness result of positive radial solutions of elliptic equations obtained by Shioji-Watanabe (JDE 255 (2013)). In particular, for an elliptic problem in two dimensional space, we obtained a new uniqueness result, and we show that we can apply it to the Haraux-Weissler equation in two dimensional space. Moreover, for some elliptic problems, we study the nondegeneracy of the unique positive radial solution in a radial function space under almost same assumptions for the uniqueness. We also study its nondegeneracy even in a space which is not restricted to be radial.
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| Academic Significance and Societal Importance of the Research Achievements |
微分方程式を用いてモデルを記述することが多い自然科学や工学において、考えている方程式に対し、解は存在するのか、存在する場合、解は一意なのかあるいは多数存在するのかは重要な問題である。微分方程式論の研究において、解の存在と一意性・多重性は幅広く研究されており、研究成果は微分方程式論の発展のために寄与するものである。
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Report
(6 results)
Research Products
(22 results)
