Exponential solutions of equation \(\dot y(t)=\beta(t)[y(t-\delta)-y(t-\tau)]\)
type: Item
instance of: scholarly article
title: Exponential solutions of equation \(\dot y(t)=\beta(t)[y(t-\delta)-y(t-\tau)]\)
zbMATH Open document ID: 1058.34099
author: Josef Diblík
author: Miroslava Růžičková
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-10T00:00:00Z
review text: The authors study the asymptotic behaviour as \(t\to\infty\) of the first-order differential equation with two deviating arguments \[ \dot y= \beta(t)[y(t -\delta)- y(t- \tau)].\tag{\(*\)} \] The relation between solutions of \((*)\) and of the inequality \[ \dot y\leq\beta(t)[y(t- \delta)- y(t- \tau)]\tag{\(**\)} \] plays a basic role. A criterion for representing solutions of \((*)\) in exponential form is obtained. A sufficient condition for the existence of unbounded solutions is derived, and an illustrative example is given.
reviewed by: Bolis Basit
Mathematics Subject Classification ID: 34K25
zbMATH DE Number: 2085927
zbMATH Keywords: discrete delay
zbMATH Keywords: two deviating arguments
zbMATH Keywords: exponential solution
zbMATH Keywords: unbounded solution
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.02.036
OpenAlex ID: W1964586559
cites work: Asymptotically diagonal delay differential systems
cites work: Convergence in asymptotically autonomous functional differential equations
cites work: More on linear differential systems with small delays
cites work: Criteria for asymptotic constancy of solutions of functional differential equations
cites work: Q5728644
cites work: Asymptotic constancy for nonhomogeneous linear differential equations with unbounded delays
cites work: \(L^p\) perturbations in delay differential equations
cites work: Q4953554
cites work: The asymptotic bounds of solutions of linear delay systems
cites work: A change of variables in the asymptotic theory of differential equations with unbounded delays
cites work: Some equations modelling growth processes and gonorrhea epidemics
cites work: Q4214730
cites work: Q4000352
cites work: Q4894463
cites work: \(L^ 2\)-perturbation of a linear delay differential equation
cites work: Special solutions of neutral functional differential equations
cites work: Q3198179
cites work: Asymptotic constancy for systems of delay differential equations
cites work: Asymptotic convergence criteria of solutions of delayed functional differential equations
cites work: Asymptotic representation of solutions of the equation \(\dot y(t)=\beta(t)[y(t)-y(t-\tau(t))]\)
DOI: 10.1016/J.JMAA.2004.02.036
description: scientific article; zbMATH DE number 2085927