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VOL. 53 | 2009 Periodic solutions of periodic difference equations
Tetsuo Furumochi, Masato Muraoka

Editor(s) Saber Elaydi, Kazuo Nishimura, Mitsuhiro Shishikura, Nobuyuki Tose

## Abstract

In this paper, we discuss the existence of periodic solutions of the periodic difference equation $$x(n + 1) = f(n, x(n)),\ \ n \in \mathbf{Z}$$ and the periodic difference equation with finite delay $$x(n + 1) = f(n, x_n),\ \ n \in \mathbf{Z},$$ where $x$ and $f$ are $d$-vectors, and $\mathbf{Z}$ denotes the set of integers. We show the existence of periodic solutions by using Browder's fixed point theorem, and illustrate an example by using a boundedness result due to Shunian Zhang.

## Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1182.39013
MathSciNet: MR2582404

Digital Object Identifier: 10.2969/aspm/05310051

Subjects:
Primary: 39A11