Asymptotic representation of solutions of the equation \(\dot y(t)=\beta(t)[y(t)-y(t-\tau(t))]\)
type: Item
instance of: scholarly article
title: Asymptotic representation of solutions of the equation \(\dot y(t)=\beta(t)[y(t)-y(t-\tau(t))]\)
zbMATH Open document ID: 0892.34067
author: Josef Diblík
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-07-05T00:00:00Z
review text: The equation considered is the following differential difference equation \[ \dot{y}=\beta(t) [y(t)-y(t-\tau(t))], \tag{1} \] where \(\tau\in C(I_{-1},{\mathbb{R}}^+)\), \(I_{-1}=[t_{-1},\infty)\), \(t_{-1}=t_0-\tau(t_0)\), \(t_0\in{\mathbb{R}}\), \(t\mapsto t-\tau(t)\) is increasing, \(\tau(t)\geq\widetilde{\tau}\) for all \(t\), \(\widetilde{\tau}= \text{ const}>0\), \(\beta\in C([t_0,\infty),{\mathbb{R}}^+)\). The author proves theorems on the existence of solutions of (1) tending to infinity as \(t\to\infty\), and of solutions with the range in \([C_1,C_2]\) for any \(C_1<C_2\). Exponential estimates and comparison theorems are also discussed.
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34K99
zbMATH DE Number: 1115466
zbMATH Keywords: differential-difference equations
zbMATH Keywords: asymptotic behavior of solutions
reviewed by: R. R. Akhmerov
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5709
OpenAlex ID: W2052022879
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DOI: 10.1006/JMAA.1997.5709
description: scientific article; zbMATH DE number 1115466