2023 Fiscal Year Final Research Report
Exact number of solutions and bifurcation phenomena to two-point boundary value problems
Project/Area Number |
19K03595
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Review Section |
Basic Section 12020:Mathematical analysis-related
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Research Institution | Tohoku University (2020-2023) Okayama University of Science (2019) |
Principal Investigator |
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Project Period (FY) |
2019-04-01 – 2024-03-31
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Keywords | 境界値問題 / 楕円型方程式 / 球対称解 / 一意性 / 多重存在性 / 準線形 / 解曲線の長さ / 漸近挙動 |
Outline of Final Research Achievements |
New uniqueness and multiple existence results were derived for radially symmetric solutions of elliptic partial differential equations. The asymptotic behavior of radially symmetric solutions of quasilinear elliptic equations was investigated. The asymptotic behavior of solutions of equations with p-Laplace operators and the asymptotic behavior and monotonicity of eigenvalues were also studied. New results were also obtained on the existence of solutions to elliptic equations with general differential operators. Furthermore, the stability of solutions asymptotic to the origin of a two-dimensional nonautonomous differential system was evaluated in terms of the length and fractal dimension of the solution trajectory.
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Free Research Field |
境界値問題
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Academic Significance and Societal Importance of the Research Achievements |
円環領域における楕円型偏微分方程式の正値解の一意性について、これまで未解決であった部分について一定の答えを与えることができた。ある準線形の自励型常微分方程式系の平衡解の線形化に対応する新しい理論を構築した。これは楕円型偏微分方程式の解析などの様々な応用が見込まれるものである。一般的な微分作用素をもつ楕円型方程式の研究は、現在、活発に研究が行われており、本研究により、様々な微分作用素を統一的に扱う方法が提示され、今後の多くの研究で、その応用が期待される。
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