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

Hou Yu Zhao, Michal Fečkan


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 $m=1,2, \ldots, k.$.


iterative differential equation; periodic solutions; fixed point theorem

Full Text:


ISSN: 1331-0623 (Print), 1848-8013 (Online)