Periodic solutions for a class of differential equation with delays depending on state

Abstract

In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of periodic solutions of a class of iterative differential equation $$x'(t)=\sum_{m=1}^k\sum_{l=1}^\infty C_{l, m}(t)(x^{[m]}(t))^l+G(t),$$ where $x^{[m]}(t)$ denotes $m$th iterate of $x(t)$ for $m=1,2, \ldots, k.$.