非线性无穷时滞微分系统的稳定性

Stability for Nonlinear Differential Systems with Infinite Delay

本文主要内容是：（１）在局部条件下，建立了一类具有无穷时滞的非线性的正、反向积分微分不等式；（２）结合常数变易法和Ｌｉａｐｕｎｏｖ函数法（不必寻找Ｐ－函数），利用所建立的不等式研究了非线性无穷时滞微分系统的稳定性；（３）举例说明了本文定理的应用和优点。

The main purpose of this paper is as follows:(1)to establish some nonlinear integro-differential inequalities with infinite delay and theinverse inequalities under the local conditions;(2)to study the stability of the nonlinear differen-tial systems with infinite delay by using the method of variation of constants, Liapunov function(need not find P-function)and the inequalities established;(3)to give some examples to showthe application and advantage of the theorems in the paper.