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Research of equations with time delay

时滞方程的研究

基本信息

批准号：
09640235
负责人：
MURAKAMI Satoru
金额：
$ 1.6万
依托单位：
Okayama University of Science
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640235/
关键词：
Functional differential equations Processes Functional difference equations Stability properties Periodic solutions Almost periodic solutions Asymptotic behavior Volterra systems 有界解

项目摘要

Head investigator and 8 investigators studied some qualitative properties of solutions in equations with time delay, and obtained many results on the subject. The contents of a part of results obtained are summarized in the following :First we treated functional differential equations which are typical ones as equations with time delay, and obtained some results on stability properties and the existence of almost periodic solutions under some conditions. Moreover, applying the degree theory we established the existence of periodic solutions for some functional differential equations with diffusion which appear as crucial models in the field of mathematical biology.Next we treated functional difference equations and characterized the summability of the fundamental solution in connection with the uniform asymptotic stability property for the solu tion. Also, we established the representation theorem of solutions in phase space, and discussed the existence of bounded solutions and the asymptotic equivalence of solutions by applying the representation theorem.Furthermore, we treated processes which belong to a more wide class than equations with time delay, and developing a part of qualitative theory for processes, we applied general results obtained for processes to get some stability properties for functional differential equations and to establish the existence of almost periodic solutions for wave equations.

主要研究者和8名研究者研究了时滞方程解的一些定性性质，得到了许多结果。所获得的部分结果的内容概括如下：首先，我们将典型的泛函微分方程视为时滞方程，并在一定条件下获得了稳定性和概周期解存在性的一些结果。其次，利用度理论证明了生物数学中一类重要模型的周期解的存在性，并讨论了一类泛函差分方程的基本解的可和性，以及解的一致渐近稳定性.建立了相空间中解的表示定理，并应用该表示定理讨论了有界解的存在性和解的渐近等价性，进而讨论了比时滞方程更广泛的一类过程，发展了过程的一部分定性理论，应用对过程的一般性结果，得到了泛函微分方程的一些稳定性性质，并建立了波动方程概周期解的存在性。