Oscillations of some delay differential equations with periodic coefficients
type: Item
instance of: scholarly article
title: Oscillations of some delay differential equations with periodic coefficients
zbMATH Open document ID: 0751.34038
DOI: 10.1016/0022-247X(91)90161-R
author: Ch. G. Philos
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-26T00:00:00Z
review text: The author considers the following delay differential equations: \((E)\;x'(t)+a(t)[px(t-\tau)+qx(t-\sigma)]=0\), \((\overline E)\;x'(t)+f(t)x(t- \tau)-g(t)x(t-\sigma)=0\), \(t\geq 0\), where \(a,f,g\) are continuous periodic functions with a period \(\omega>0\), \(p,q,\tau(\geq 0)\), \(\sigma(\geq 0)\in R\) and \(\tau=\mu\omega\), \(\sigma=\nu\omega\) for some nonnegative integers \(\mu,\nu\). Denote \(A={1\over\omega}\int^ \omega_ 0a(t)dt\). Theorem 1. The following statements are equivalent: (I) All solutions of \((E)\) are oscillatory. (II) The equation \(\lambda+A(p\exp(- \lambda\tau)+q\exp(-\lambda\sigma))=0\) has no real roots. Moreover, there are given sufficient conditions for (i) every nonoscillatory solution of \((\overline E)\) to tend to zero as \(t\to\infty\); (ii) all solutions of \((\overline E)\) to be oscillatory.
reviewed by: Pavol Marušiak
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 55696
zbMATH Keywords: delay differential equations
zbMATH Keywords: oscillatory
zbMATH Keywords: nonoscillatory solution
MaRDI profile type: Publication
cites work: Oscillation criteria in delay equations
cites work: On Oscillations of Some Retarded Differential Equations
cites work: Necessary and sufficient conditions for oscillation of delay equations with constant coefficients
cites work: When all solutions of \(x'=-\Sigma q_ i(t)x(t-T_ i(t))\) oscillate
cites work: Q3961172
cites work: Sharp conditions for oscillations caused by delays
cites work: Oscillations of Neutral Delay Differential Equations
cites work: Necessary and Sufficient Conditions for Oscillations of Higher Order Delay Differential Equations
cites work: Q3954160
cites work: Q4836479
cites work: On the Oscillation of Differential Equations with Periodic Coefficients
cites work: Q4081674
Recommended article: Q5752885
Recommended article: Oscillations of delay difference equations with oscillating coefficients
Recommended article: Oscillation of delay dynamic equations with oscillating coefficients
Recommended article: Q5690011
Recommended article: Oscillation of first order nonlinear delay differential equations with periodic coefficients
Recommended article: Oscillations of delay differential equations with variable coefficients
Recommended article: Periodic and almost periodic oscillations in a delay differential equation system with time-varying coefficients
Recommended article: Oscillations of certain delay integro-differential equations
Recommended article: Q5688564
description: scientific article; zbMATH DE number 55696