Convergence of the solutions of the equation \(\dot y(t) = \beta(t)[y(t-\delta)-y(t-\tau)]\) in the critical case
type: Item
instance of: scholarly article
title: Convergence of the solutions of the equation \(\dot y(t) = \beta(t)[y(t-\delta)-y(t-\tau)]\) in the critical case
zbMATH Open document ID: 1125.34059
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-04-26T00:00:00Z
review text: This paper deals with the asymptotic behavior of a first order linear homogeneous differential equation with double delay of the form \[ y'(t)=\beta(t)[y(t-\delta)-y(t-\tau)], \] where \(\delta\) and \(\tau\) are positive with \(\tau>\delta\); \(\beta\in C([t_0-\tau,\infty),\mathbb R^+)\). The authors especially deal with the so called critical case with respect to the function \(\beta\) which separates the case when all solutions are convergent and the case when there exist divergent solutions. For coefficients below the critical function, a strictly increasing and bounded solution is constructed, which characterizes the asymptotic convergence of all solutions.
reviewed by: Meng Fan
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34K12
Mathematics Subject Classification ID: 34K06
zbMATH DE Number: 5146744
zbMATH Keywords: convergent solution
zbMATH Keywords: two delayed arguments
author: Josef Diblík
author: Miroslava Růžičková
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.10.001
OpenAlex ID: W2014969630
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DOI: 10.1016/J.JMAA.2006.10.001
description: scientific article; zbMATH DE number 5146744