2007 Fiscal Year Final Research Report Summary
Birkohoff theory for non-autonomous differential equations with delay
| Project/Area Number |
16540139
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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 | Chiba University |
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Principal Investigator |
HINO Yoshiyuki Chiba University, Graduate School of Science, 教授 (70004405)
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| Co-Investigator(Kenkyū-buntansha) |
INABA Takashi Chiba University, Graduate School of Science, Professor (40125901)
ISHIMURA Ryuichi Chiba University, Graduate School of Science, Professor (10127970)
OKADA Yasunoti Chiba University, Graduate School of Science, Associate Professor (60224028)
NAITO Toshiki University of Electronics and Infomatics, 電気通信学部, Professor (60004446)
MURAKAMI Satoru University of Okayama Science, 理学部, Professor (40123963)
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| Project Period (FY) |
2004 – 2007
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| Keywords | dynamical system / minimal set / functional differential equation / boundedness / stability |
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| Research Abstract |
There are many methods to discuss nonlinear oscillations for functional differential equations with infinite delay. Dynamical systems are very important for equations with uniqueness property. Another methods are analytic methods. Analytic methods are very difficult, because there are many methods for the case the dimension of phase spaces is infinite or infinite.
In this reports, we consider the only the property of solutions which is called processes. This idea is based by Brown University that is the main place of LaSalle's invariant principle. We have the followings for the above problem: (i) Application to functional differential equations and evolution equations. (ii) Applicaions to partial differential equations. (iii) Construction of general dynamical systems (iv) Construction of the best topology for dynamical systems.
Thus we could discuss many results.
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