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
Publication date:
30.5.2018.
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