几类泛函微分方程的稳定性比较研究

Comparative Study on the Stability of Several Classes of Functional Differential Equations

泛函微分方程是对各种具有复杂变元的微分方程和带有各种滞后量的积分微分方程等的抽象概括,其稳定性研究在现代化的科学研究中具有重要的作用;在此,就中立型泛函微分方程、非线性泛函微分方程和随机时滞泛函微分方程的稳定性进行了探讨;不同类型的泛函微分方程采用的数值方法尽管有相似之处,但也有一些区别;无论哪种方法,都旨在为泛函微分方程的稳定性研究提供可靠的理论保障。

Functional differential equations are abstract generalizations of all kinds of differential equations with complex arguments and integro-differential equations with various delays,whose stability research plays an important role in modern scientific research. This paper discusses the stability of neutral functional differential equations, nonlinear functional differential equations and stochastic delay functional differential equations.Although the numerical methods used in different types of functional differential equations are similar,there are some differences. Either method is designed to provide a reliable theoretical guarantee for the researches on the stability of functional differential equations.