2009 Fiscal Year Final Research Report
Study of stability properties for positive linear equations with delay and related topics
| Project/Area Number |
19540203
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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 | Okayama University of Science |
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Principal Investigator |
MURAKAMI Satoru Okayama University of Science, 理学部, 教授 (40123963)
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| Co-Investigator(Kenkyū-buntansha) |
KAMIYA Shigeyasu 岡山理科大学, 工学部, 教授 (80122381)
HAMAYA Yoshihiro 岡山理科大学, 総合情報学部, 教授 (40228549)
NAGABUCHI Yutaka 岡山理科大学, 理学部, 教授 (60252607)
TANAKA Satoshi 岡山理科大学, 理学部, 准教授 (90331959)
SHIMENO Nobukazu 岡山理科大学, 理学部, 准教授 (60254140)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 関数方程式 / 関数微分方程式 / 正の方程式 / 安定性 / 漸近挙動 |
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| Research Abstract |
We studied qualitative properties of solutions in functional differential equations, integrodifferential equations and Volterra difference equations which are typical ones of equations with delay. Applying the variation-of-constants formula in the phase space for functional differential equations, we obtained a result on the behavior of solutions for equations with a perturbation. Also, we established a result on the existence of several invariant manifolds for nonlinear functional differential equations. Furthermore, treating integrodifferential equations mainly, we investigated the positivity of equations, and obtained a criterion on stabilities for positive equations.
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