2011 Fiscal Year Final Research Report
Asymptotic property of solutions of delay equations and spectral analysis
| Project/Area Number |
21740103
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | 時間遅れ / 微分方程式 / 差分方程式 / 漸近安定性 |
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| Research Abstract |
In this research we have studied the asymptotic property of solutions of delay equations and spectral analysis, and have presented the following main results.(1) We have established some asymptotic stability conditions for the zero solution of linear integro-differential systems and linear difference systems with diagonal or off-diagonal delays. In particular, we have showed that stability switches appear in linear integro-differential systems as a parameter of diagonal delays increases under certain conditions.(2) For linear Volterra difference equations with infinite delay, we have obtained an explicit representation form of the projection on the center-unstable subspace in the phase space to get an asymptotic formula of the solutions. As an application, we have easily calculated some asymptotic periodic solutions of concrete equations.
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