一类多时滞微分积分方程周期解的存在性和唯一性

On the Existence and Uniqueness of Periodic Solutions of a Kind of Differential-integro Equations with Multiple Delays

考虑一类具有连续时滞和离散时滞的非线性微分积分方程■周期解的存在性和唯一性问题,通过利用非线性泛函分析方法研究此类方程,获得其周期解存在且唯一性的充分条件,得到两个新的定理,这些定理推广了已有的结果.

In this paper we discuss the existence and uniqueness of periodic solution of a kind of continuous time-delay and discrete time-delay nonlinear differential integral equation x＇（t）=A（t）x（t）＋∫-∞^tC（t,s）x（s）ds＋n∑i=1fi（t,x（t-Ti（t）））By using non-linear functional analysis method for such equations, we have obtained the sufficient condition for the existence and uniqueness of periodic solutions and got two new theorems, which expand the existing results.