2015 Fiscal Year Final Research Report
Precise asymptotic analysis of solutions of nonlinear differential equations by means of regular variation: The theoretical face and back sides for oscillation theory
| Project/Area Number |
23540218
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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 |
Basic analysis
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| Research Institution | Kumamoto University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Keywords | 微分方程式論 / 振動理論 |
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| Outline of Final Research Achievements |
The purpose of this research subject is devoted to the asymptotic analysis of the nonoscillatory behavior of several types of the nonlinear differential equations. Our main results obtained are as belows.
(1) The existence and the asymptotic behavior for the large value of the variable of the positive solutions of generalized Thomas-Fermi equation are proved. (2) We establish a sharp condition of the existence of generalized regularly varying functions (in the sense of Karamata) of self-adjoint functional differential equation. (3) We devote to the asymptotic analysis of a class of the third order sublinear differential equation. (4) We demonstrate that the method of regular variation can be effectively applied to fourth order quasilinear differential equations. (5) We show that an application of the theory of regular variation gives the possibility of determining the existence and precise asymptotic behavior of positive solutions of the third order nonlinear differential equation
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| Free Research Field |
数物系科学
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