Original scientific paper

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

Hou Yu Zhao ; School of Mathematics, Chongqing Normal University, P. R. China
Michal Fečkan ; Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynska dolina, Bratislava, Slovakia

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

Keywords

iterative differential equation; periodic solutions; fixed point theorem

Hrčak ID:

192116

URI

https://hrcak.srce.hr/192116

Publication date:

30.5.2018.

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