2003 Fiscal Year Final Research Report Summary
Existence of Almost periodic solutions for functional differential equation
| Project/Area Number |
14540152
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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, Faculty of Science, Professor, 理学部, 教授 (70004405)
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| Co-Investigator(Kenkyū-buntansha) |
OKADA Yasunoti Chiba University, Faculty of Science, Associate Professor, 理学部, 助教授 (60224028)
ISHIMURA Ryuichi Chiba University, Faculty of Science, Professor, 理学部, 教授 (10127970)
INABA Takashi Chiba University, Graduate School of Science and Technology, Professor, 大学院・自然科学研究科, 教授 (40125901)
MURAKAMI Satoru Univ.of Okayama Science, Professor, 理学部, 教授 (40123963)
NAITO Toshiki Univ.of Electronics and Informatics, Professor, 電気通信学部, 教授 (60004446)
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| Project Period (FY) |
2002 – 2003
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| Keywords | functional differential equations / almost periodic solution / periodic solution / Bohr Spectrum / constant formula |
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| Research Abstract |
If we consider an evolution equations which is a generalization of partial differential equations with infinite delay, The phase space has two types, that is, one is a uniform fading memory space and the other is a fading memory space. In this report, we have the followings for the above equations :
(i)Phase space and decompositions.
(ii)Liapunov's method and existence theorems of almost periodic solutions.
(iii)existence theorem for linear systems.
(iv)existence of almost periodic solution for nonlinear systems.
In particular, existence theorems of almost periodic solutions and almost automorphic solutions are shown by using the constant formula. These are generalizations of Massera Type theorems for periodic systems. And, Bohr spectrum of the solutions are inherited from that of perturbed terms.
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