Global behavior of the max-type difference equation \(x_{n}=\max \{\frac{A_1}{x^{\alpha_1}_{n-m\_1}}, \frac{a_2}{x^{\alpha_2}\_{n-m_2}},\dots,\frac{A_k}{x^{\alpha_k}\_{n-m_k}} \}\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 1250.39009
author: Bin Qin
author: Taixiang Sun
author: Hongjian Xi
publication date: 2012-07-20T00:00:00Z
full work available at URL: index.html
Mathematics Subject Classification ID: 39A20
Mathematics Subject Classification ID: 39A22
zbMATH DE Number: 6058728
zbMATH Keywords: MAX-type difference equation
zbMATH Keywords: positive solution
zbMATH Keywords: convergence
MaRDI profile type: Publication
title: Global behavior of the max-type difference equation \(x_{n}=\max \{\frac{A_1}{x^{\alpha_1}_{n-m\_1}}, \frac{a_2}{x^{\alpha_2}\_{n-m_2}},\dots,\frac{A_k}{x^{\alpha_k}\_{n-m_k}} \}\)
published in: International Journal of Mathematical Analysis (Ruse)
review text: The authors show that any positive solution of the difference equation NEWLINE\[NEWLINE x_{n}=\max\left\{\frac{A_1}{x^{\alpha_1}_{n-m_1}},\frac{A_2}{x^{\alpha_2}_{n-m_2}},\dots,\frac{A_k}{x^{\alpha_k}_{n-m_k}}\right\}, \;\;n=0,1,\dots, NEWLINE\]NEWLINE where \(A_i>0\), \(\alpha_i\in(0,1)\), \(m_i\) is a natural number for \(i=1,\dots,k\), \(A_i^{\frac{1}{1+\alpha_i}}\leq A_{i+1}^{\frac{1}{1+\alpha_{i+1}}}\) for \(i=1,\dots,k-1\), converges to \(A_k^{\frac{1}{1+\alpha_k}}\).
reviewed by: Oleg Anashkin
description: scientific article; zbMATH DE number 6058728