2023 Fiscal Year Final Research Report
Asymptotic analysis of quasilinear ordinary differential equations and its application to partial differential equations
| Project/Area Number |
21K03307
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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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| Review Section |
Basic Section 12020:Mathematical analysis-related
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| Research Institution | Gifu University |
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Principal Investigator |
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| Project Period (FY) |
2021-04-01 – 2024-03-31
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| Keywords | 漸近挙動 / 正値解 / 半分線形常微分方程式 / 準線形常微分方程式 |
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| Outline of Final Research Achievements |
Mainly, asymptotic theory of solutions of quasilinear ordinary differential equations were investigated. More precisely, the following themes have been studied: 1. To find the asymptotic forms of perturbed half-linear ordinary differential equations with constant coefficients; 2. To find the asymptotic forms of positive solutions of super-homogeneous, quasilinear ordinary differential equations with critical coefficients; 3. To establish necessary and/or sufficient conditions for higher order quasilinear ordinary differential equations to have singular solutions; 4. To establish necessary and/or sufficient conditions for higher order quasilinear ordinary differential equations to have Kneser solutions.
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| Free Research Field |
微分方程式論
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| Academic Significance and Societal Importance of the Research Achievements |
1. 主テーマである半分線形方程式は線形方程式の一般化にあたる．研究手法等も線形方程式に対するそれの一般化にあたるであろう．数学理論がどのように普遍化・一般化されていくのかをこの研究を通じて俯瞰することができるであろう．
２．自然現象・社会現象を記述する数理モデルは，第一段階としては「線形近似」という見方で定式化されることが多い．しかし，より詳細にみると，本質的に非線形性になっているということもある．この研究ではそのような現象を数学的に解析する手法をいくつか提案している．
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