A survey of differential equations with piecewise continuous arguments
A survey of differential equations with piecewise continuous arguments
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DOI：
10.1007/bfb0083475
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发表时间：
1991-08
期刊：
影响因子：
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通讯作者：
K. Cooke;J. Wiener
中科院分区：
文献类型：
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作者：
K. Cooke;J. Wiener
到目前为止，泛函微分方程的一般理论和基本结果已经得到了深入的探讨，可以在海尔的名著和许多作者随后的文章中找到。然而，仍然需要对特殊方程进行研究，这些方程可能具有有趣的性质，并为更抽象的理论提供见解。在这篇回顾文章中，我们将描述我们和其他人在过去几年里所做的一些关于微分方程的工作，我们称之为分段连续参数方程，或EPCA。我们的注意力是由AD Myshkis b[23]的一篇文章引导到这些方程的，他观察到对于具有分段常数或分段连续的滞后参数的微分方程不存在实质性的理论。从那时起，几位作者研究了这种类型的方程。本文的目的是对这方面的研究现状进行简要的综述，并指出进一步研究的方向。
The general theory and basic results for functional differential equations have by now been thoroughly explored and are available in the famous book of Hale [19] and subsequent articles by many authors. Nevertheless, there is still need for investigation of special equations, which may have interesting properties and provide insight into the more abstract theory. In this review article, we shall describe some of the work that has been done by us and others over the last few years on the differential equations that we call equations with piecewise continuous arguments, or EPCA. Our attention was directed to these equations by an article of AD Myshkis [23], who observed that a substantial theory did not exist for differential equations with lagging arguments that are piecewise constant or piecewise continuous. Since that time several authors have investigated equations of this type. The purpose of this article is to give a brief survey of the present status of this research and to point out some directions for further study.