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 with unbounded delay, and the existence, uniqueness and stability of the periodic solution are dealt with unitedly. First we establish the suitable delay-differential inequality, then study seperately the problems of periodic solution for the systems with bounded delay, with unbounded delay and the Volterra integral-differential systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré's periodic operator in the different phase spaces. A series of simple criteria for the existence, uniqueness and stability of these systems are obtained.