2012 Fiscal Year Final Research Report
Inverse problems and nonlinear integral transforms
| Project/Area Number |
21540165
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo University of Marine Science and Technology |
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Principal Investigator |
KAMIMURA Yutaka 東京海洋大学, 海洋科学技術研究科, 教授 (50134854)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 関数方程式 / 逆問題 / 非線形大域理論 |
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| Research Abstract |
We establish a theory of a nonlinear integral transform and obtain a global theorem for an inverse problem in bifurcation theory. Based upon the result we consider a problem of determining a nonlinearity of an autonomous differential equation of a period function, namely, a relation between periods and amplitudes to prove a global existence of nonlinear terms realizing a prescribed, Lipschitz continuous period function and characterize the nonlinear terms. This gives a complete answer to a classical inverse problem in a nonlinear autonomous oscillation.
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