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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

Rights: Copyright © 2009 Mathematical Society of Japan

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