具无限时滞中立型泛函微分方程解的稳定性与有界性

Stability and Boundedness of Neutral Functional Differential Equations with Infinite Delay

以(Ch,∣·∣h)相空间为基础,研究了具有无限时滞中立型泛函微分方程解的稳定性和有界性,建立了方程解为一致稳定,一致渐近稳定的充要性判据;证明了当方程右端泛函满足Lipschitz条件时,解的一致渐近稳定性蕴涵了有界解的存在性,推广了文献[4-6]中已有的相关结果.

With the help of the phase space （Ch,│·│h）, sufficient and necessary criterias are established for the uniform stability and uniformly asymptotic stability of solutions to neutral functional differential equations with infinite delay. In addition, the author also prove that the uniformly asymptotic stability of solutions implies the existence of the bounded solutions when the equation satisfies Lipschitz assumption.