Large time behavior of a linear difference equation with rationally non-related delays
type: Item
instance of: scholarly article
title: Large time behavior of a linear difference equation with rationally non-related delays
zbMATH Open document ID: 1269.39001
published in: Journal of Mathematical Analysis and Applications
publication date: 2013-02-21T00:00:00Z
review text: The author studies the equation with discrete delays \[ x\left( t\right) =\sum_{j=1}^{N}a_{j}x\left( t-r_{j}\right),~ t\geq 0, \] where \(a_{j}>0,\) \(1\leq j\leq N\) and \(0<r_{1}<\dots<r_{N}.\) The case of rationally non-related delays is considered. Under some specific hypotheses, he finds the limit as \(t\rightarrow\infty\) of \(x\left( t\right) e^{-\lambda t}\), where \(\lambda\) is the unique real root of the characteristic function \(h\) defined through \[ h\left( s\right) =0, ~h\left( s\right) =1- \sum_{j=1}^{N}a_{j}e^{-sr_{j}}. \] If the sum of the coefficients in the above equation is one, then he deduces a result on asymptotic constancy.
Mathematics Subject Classification ID: 39A06
Mathematics Subject Classification ID: 39A22
zbMATH DE Number: 6138119
zbMATH Keywords: linear difference equation
zbMATH Keywords: rationally non-related delays
zbMATH Keywords: large time behavior
zbMATH Keywords: characteristic equation
zbMATH Keywords: dominant root
zbMATH Keywords: asymptotic constancy
author: Mihály Pituk
reviewed by: Narcisa Apreutesei
MaRDI profile type: Publication
full work available at URL: j.jmaa.2012.11.014
OpenAlex ID: W2085558672
DOI: 10.1016/J.JMAA.2012.11.014
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description: scientific article; zbMATH DE number 6138119