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

Hou Yu Zhao; Michal Fečkan

Vol. 23 No. 1 (2018)

Regular Articles

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

Published 2017-07-11

Hou Yu Zhao
Michal Fečkan

Hou Yu Zhao
School of Mathematics, Chongqing Normal University

Michal Fečkan
Department of Mathematical Analysis and Numerical Mathematics Comenius University Bratislava

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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

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