Eigenvalue problems for non-homogeneous elliptic operators
| Project/Area Number |
15K17577
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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 |
Mathematical analysis
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
Tanaka Mieko 東京理科大学, 理学部第一部数学科, 講師 (00459728)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 非線形固有値問題 / 非同次な楕円型作用素 / 楕円型作用素 / 正値解 / 符号変化解 / 解の正値性 |
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| Outline of Final Research Achievements |
We analyzed the generalized eigenvalue problem of the operator (p, q) -Laplacian which can be made by combining two elliptic operators p-Laplacian and q-Laplacian, in particular, two parameters. The eigenvalue problem here is mainly to analyze the parameters for which non-trivial solutions exist or not. In this research, we determined the range of parameters in which positive solutions exist completely, and provided the existence of parameters in which there is a sign-changing solution.
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| Academic Significance and Societal Importance of the Research Achievements |
最近では、本研究で扱った(p,q)-Laplace作用素を含む微分方程式が多く研究されており、最近の (p,q)-Laplace 方程式の研究についてまとめたサーベー論文（２０１７年出版）において本研究成果も大きく取り上げられた。この結果、(p,q)-Laplacian の他の境界条件に変えた場合の固有値問題への研究が複数始められ現在では幾つかの結果が得られている。また、本研究結果を用いて、関連した方程式への研究成果も得られている。
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Report
(5 results)
Research Products
(16 results)
