| Project/Area Number |
23740113
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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 |
Basic analysis
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| Research Institution | Okayama University of Science |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | ２点境界値問題 / 正値解 / 球対称解 / 一意性 / フラクタル次元 / 国際情報交換 / 振動解 / 解の個数 / クロアチア / 国際研究者交流 / 台湾 |
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| Research Abstract |
In this study, two-point boundary value problems for nonlinear ordinary differential equations were considered. The positive solution is a kind of nonoscillatory solutions. The symmetry-breaking for positive solutions was proved by finding the Morse index of positive solutions. Then the existence of positive symmetry solutions and positive asymmetry solutions was shown, and therefore, a result of the nonuniqueness of positive solutions was established. A sufficient condition is obtained for the existence of exact two positive solutions of problems with one dimensional p-Laplacian. The fractal dimension of radial oscillatory solutions for a class of elliptic partial differential equations was found.
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