2013 Fiscal Year Final Research Report
The number of nonoscillatory solutions and the length and the fractal dimension for two-point boundary value problems
| 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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| 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 |
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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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