On piecewise constant delay differential equations
type: Item
instance of: scholarly article
title: On piecewise constant delay differential equations
zbMATH Open document ID: 0913.34054
DOI: 10.1016/0022-247X(92)90103-K
author: K. N. Jayasree
author: Sadashiv Deo
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-04-01T00:00:00Z
review text: For systems of differential delay equations \[ z'(t) = A(t)z(t) + B(t)z([t]) + c(t) \] existence and uniqueness of solutions is proved by means of successive approximations, a variation of parameters formula together with its relation to the corresponding formula for \(B = 0\) is established, and results on asymptotic stability of the zero solution for related semilinear problems with nonlinear terms that become small as \( t \to \infty\) are proved. In addition, the paper contains a Gronwall type estimate for solutions to related integral inequalities, sufficient criteria for the oscillatory behavior of solutions, and similar results for solutions to scalar equations with two delays of the form \(z'(t) = az(t) + bz([t]) + cz(t-\tau) + f(t)\).
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34K11
zbMATH DE Number: 150623
zbMATH Keywords: differential delay equations
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: solutions
zbMATH Keywords: asymptotic stability
zbMATH Keywords: semilinear problems
zbMATH Keywords: Gronwall type estimate
zbMATH Keywords: integral inequalities
zbMATH Keywords: oscillatory behavior
MaRDI profile type: Publication
cites work: Oscillatory properties of first order linear functional differential equations
cites work: Q3657815
cites work: Retarded differential equations with piecewise constant delays
cites work: Q5584128
cites work: Q4051163
cites work: Oscillations in systems of differential equations with piecewise constant argument
description: scientific article; zbMATH DE number 150623