A change of variables in the asymptotic theory of differential equations with unbounded delays
type: Item
instance of: scholarly article
title: A change of variables in the asymptotic theory of differential equations with unbounded delays
zbMATH Open document ID: 1016.34077
DOI: 10.1016/S0377-0427(01)00500-3
author: Jan Čermák
published in: Journal of Computational and Applied Mathematics
publication date: 2002-08-22T00:00:00Z
review text: The author deals with asymptotic properties of solutions to the nonhomogeneous linear differential equation \[ \dot x(t)= ax(\tau(t))+ bx(t)+ f(t)\tag{1} \] with nonzero real scalars \(a\), \(b\), and unbounded lag. The key techniques here is based on a change of the independent and dependent variables in equation (1) into a more suitable form. This work is closely related to \textit{E. B. Lim} [SIAM J. Math. Anal. 9, 915-920 (1978; Zbl 0392.34035)].
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34K17
Mathematics Subject Classification ID: 39B99
zbMATH DE Number: 1787630
zbMATH Keywords: asymptotic theory
zbMATH Keywords: differential equations
zbMATH Keywords: unbounded delays
MaRDI profile type: Publication
cites work: 2.—The Matrix Functional Differential Equation y′(x) = Ay(λx) + By(x)
cites work: The asymptotic bounds of solutions of linear delay systems
cites work: On the delay differential equation y'(x) = ay(τ(x)) + by(x)
cites work: Functional-differential equations with compressed arguments and polynomial coefficients: Asymptotics of the solutions
cites work: Asymptotic representation of solutions of the equation \(\dot y(t)=\beta(t)[y(t)-y(t-\tau(t))]\)
cites work: A change of variables for functional differential equations
cites work: On the generalized pantograph functional-differential equation
cites work: Q3974156
cites work: Q4040882
cites work: Asymptotic Bounds of Solutions of the Functional Differential Equation $x'(t) = ax(\lambda t) + bx(t) + f(t),\quad 0 < \lambda < 1$
cites work: Regular solutions of the Shabat equation
cites work: Q3913730
cites work: Transformation and canonical forms of functional-differential equations
cites work: Some observations on the asymptotic behaviour of the solutions of the equation \(\dot x=A(t)x(\lambda t)+B(t)x(t)\) \(\lambda >0\)
cites work: On the limits of solutions of functional differential equations
cites work: The infinite-dimensional dressing dynamical system
cites work: Q4384844
cites work: On simultaneous Abel equations
description: scientific article; zbMATH DE number 1787630