On the Existence,Uniqueness and Stability of Periodic Solutions of Large Scale Systems with Unbounded Delay

In this paper,we consider the periodic solution problems for the systems withunbounded delay,and the existence,uniqueness and stability of the periodic solution are dealtwith unitedly.First we establish the suitable delay-differential inequality,then study seperatelythe problems of periodic solution for the systems with bounded delay,with unbounded delayand the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrixmeasure and the asymptotic fixed point theorem of poincaré’s periodic operator in the differentphase spaces.A series of simple criteria for the existence,uniqueness and stability of thesesystems are obtained.