Sufficient conditions for oscillation and nonoscillation of neutral equations
type: Item
instance of: scholarly article
title: Sufficient conditions for oscillation and nonoscillation of neutral equations
zbMATH Open document ID: 0616.34063
DOI: 10.1016/0022-0396(87)90176-8
author: E. A. Grove
author: Mustafa R. S. Kulenovic
author: G. Ladas
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: The authors obtain sufficient conditions for all solutions of the neutral delay equation \[ (1)\quad \frac{d}{dt}[x(t)-P(t)x(t-\tau)]+Q(t)x(t- \sigma)=0,\quad 0\leq P(t)\leq 1, \] to oscillate. Theorem. If \(0<K_ 1\leq q(t)\leq K_ 2\) and if \[ \inf_{\mu >0,t\geq \tau}[P(t-\tau)Q(t)Q^{- 1}(t-\sigma)e^{\mu \sigma}+\mu^{-1}Q(t)e^{\mu \sigma}]>1, \] then every solution of (1) oscillates. This result is related to the known fact that all solutions of the equation \((d/dt)[x(t)-px(t-\tau)]+qx(t- \sigma)=0\) with constant coefficients oscillate if and only if the corresponding characteristic equation \(\lambda -p\lambda e^{-\lambda \tau}+qe^{-\lambda \sigma}=0\) has no real root.
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 3998295
zbMATH Keywords: neutral delay equation
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90176-8
OpenAlex ID: W2032018317
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description: scientific article; zbMATH DE number 3998295