Oscillations of first order neutral delay differential equations
type: Item
instance of: scholarly article
title: Oscillations of first order neutral delay differential equations
zbMATH Open document ID: 0566.34056
DOI: 10.1016/0022-247X(86)90172-1
author: E. A. Grove
author: G. Ladas
author: Myron K. Grammatikopoulos
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: Consider the neutral delay differential equation \[ (*)\quad (d/dt)[y(t)+py(t-\tau)]+qy(t-\sigma)=0,\quad t\geq t_ 0 \] where \(\tau\), q and \(\sigma\) are positive constants, while \(p\in (-\infty,-1)\cup (0,+\infty)\). Theorem 1. Assume \(p<-1\). Then every nonoscillatory solution y(t) of (*) tends to \(\pm \infty\) as \(t\to \infty\). Theorem 2. Assume \(p<-1\) and \(q/(1+p)(\sigma -\tau)>1/e\). Then every solution of (*) oscillates. Theorem 3. Assume \(p>0\). Then every nonoscillatory solution y(t) of (*) tends to zero as \(t\to \infty\). Theorem 4. Assume \(p>0\). Then a necessary condition for all solutions of (*) to oscillate is that \(\sigma >\tau\). Theorem 5. Assume \(p>0\) and \(q/(1+p)(\sigma -\tau)>1/e\). Then every solution of (*) oscillates. Extensions of these results to equations with variable coefficients are also obtained.
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 3903107
zbMATH Keywords: first order neutral delay differential equations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3903107