Asymptotic and oscillatory behavior of solutions of first order nonlinear neutral delay differential equations
type: Item
instance of: scholarly article
title: Asymptotic and oscillatory behavior of solutions of first order nonlinear neutral delay differential equations
zbMATH Open document ID: 0732.34059
DOI: 10.1016/0022-247X(91)90019-V
author: John R. Graef
author: Myron K. Grammatikopoulos
author: Paul W. Spikes
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: The authors consider the (scalar) nonlinear neutral delay differential equation \([y(t)+p(t)y(t-\tau)]'-q(t)f(y(t-\sigma))=0,\) where \(q\geq 0\), \(\tau \geq 0\), \(\sigma \geq 0\) and \(uf(u)>0\), \(u\neq 0\). Two results giving hypotheses under which nonoscillatory solutions tend to zero as \(t\to \infty\) are proved. The novel feature (as compared to previous work) is that f is allowed to be nonlinear. Concerning the case where f is sublinear near the origin and superlinear at infinity it is shown, under certain additional conditions, that the equation considered is oscillatory.
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 4210607
zbMATH Keywords: oscillation theory
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: nonlinear neutral delay differential equation
reviewed by: Stig-Olof Londen
MaRDI profile type: Publication
cites work: Oscillation criteria in delay equations
cites work: Q3483629
cites work: Oscillations of first order neutral delay differential equations
cites work: Oscillation and asymptotic behavior of neutral differential equations with deviating arguments
cites work: Oscillation and asymptotic behavior of second order neutral differential equations
cites work: Oscillation and asymptotic behavior of higher order neutral equations with variable coefficients
cites work: Q4726662
cites work: Q3860165
cites work: When all solutions of \(x'=-\Sigma q_ i(t)x(t-T_ i(t))\) oscillate
cites work: Oscillations of Neutral Delay Differential Equations
cites work: Oscilations of higher-order neutral equations
cites work: Q3954160
cites work: Oscillations caused by several retarded and advanced arguments
cites work: Q3039752
cites work: Necessary and sufficient conditions for oscillations of neutral differential equations
cites work: Q3869659
cites work: Oscillating properties of the solutions of a class of neutral type functional differential equations
description: scientific article; zbMATH DE number 4210607