Periodic solutions of difference equations.
type: Item
instance of: scholarly article
title: Periodic solutions of difference equations.
zbMATH Open document ID: 1033.39018
DOI: 10.1016/S0022-247X(03)00473-6
author: Taishan Yi
author: Zhan Zhou
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-11-16T00:00:00Z
review text: For the difference equation \(x_{n+1}=\beta x_n- g(x_n)\) with \(\beta> 1\) and \(g(x)= \text{sign\,}x\) for \(x\neq 0\), \(g(0)= 1\), it is shown: For any \(m\in \mathbb{N}_0\) it has a \(2^m\)-periodic solution. If \(\beta^{2^m(2k+1)}- 2\beta^{2^m(2k-1)}\geq 1\) for \(k\in \mathbb{N}\) and some \(m\in\mathbb{N}\) it has a \((2k+1)2^m\)-periodic solution. In the case \(m= 0\) the condition is also necessary.
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 2003901
zbMATH Keywords: difference equations
zbMATH Keywords: periodic solutions
reviewed by: Lothar Berg
MaRDI profile type: Publication
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full work available at URL: s0022-247x(03)00473-6
OpenAlex ID: W2078489022
description: scientific article; zbMATH DE number 2003901