The number of solutions and the length and the fractal dimension of oscillatory solutions of two point boundary problems
| Project/Area Number |
26400182
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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 | Okayama University of Science |
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Principal Investigator |
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| Research Collaborator |
Onitsuka Masakazu
Naito Yuki
Kajikiya Ryuji
Tanaka Mieko
Kanemitsu Takanao
Shioji Naoki
Watanabe Kohtaro
Pasic Mervan
Sim Inbo
Wu Fentao
Wang Shin-Hwa
Hung Kuo-Chih
Manasevich Raul
Garcia-Huidobro Marta
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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 |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
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: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | ２点境界問題 / 正値解 / 符号変化する解 / 分岐 / 解曲線の長さ / フラクタル次元 / ボックス次元 / ２点境界値問題 / ２点境界理問題 / 国際研究者交流 |
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| Outline of Final Research Achievements |
The number of solutions and the length and the fractal dimension of oscillatory solutions of two point boundary problems are studied, and then the following results were established. Sufficient conditions for the existence of three positive solutions to two point boundary problem with a sign-changing weight function and the one-dimensional p-Lalpacian were obtained. Results on the number of solutions to the autonomous two point boundary problem with (p,q)-Lalpacian were obtained. The symmetry-breaking bifurcations for the one-dimensional Liouville type equation and the one-dimensional Henon equation were found. Results on the non-rectifiability and the box-counting dimension of solution curves of two-dimensional non-autonomous linear and half-linear differential systems were obtained.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究のテーマである２点境界値問題は、それ自身が微分方程式論のなかで重要な問題であるが、 偏微分方程式の研究でもしばしばあらわれるもので、その解の個数を知ることは基礎的かつ重要な問題である。２点境界問題の解の存在・非存在に関してこれまで膨大な量の結果が得られている一方で、その解の厳密な個数を調べることは、問題が単純な形であっても非常な困難を伴うことが多い。また、振動解のグラフの有限長性とフラクタル次元についての研究は、つい最近始まった独創的な研究である。本研究により、以上のような問題の一部が解決された。
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Report
(6 results)
Research Products
(35 results)
