Oscillation criteria for second-order delay differential equations.
type: Item
instance of: scholarly article
title: Oscillation criteria for second-order delay differential equations.
zbMATH Open document ID: 1043.34071
DOI: 10.1016/S0096-3003(02)00243-6
published in: Applied Mathematics and Computation
publication date: 2003-09-09T00:00:00Z
review text: The paper deals with the second-order nonlinear retarded differential equation \[ (r(t)| u'(t)|^{\alpha -1}u'(t))' +p(t)| u[\tau(t)]|^{\alpha -1}u[\tau(t)]=0,\tag{1} \] where \(\alpha\) is a positive number; \(r\in C^1(t_0,\infty)\), \(r(t)>0\), and \(R(t)=\int_{t_0}^tr^{-1/\alpha}(s)ds\to\infty\) as \(t\to\infty\); \(p\in C(t_0,\infty)\), \(p(t)>0\); \(\tau\in C^1(t_0,\infty)\), \(\tau(t)\leq t\), and \(\tau(t)\to\infty\) as \(t\to\infty\). The authors establish sufficient conditions for all solutions of (1) to be oscillatory in the case \(\alpha\geq 1\), and for \(0<\alpha <1\).
Mathematics Subject Classification ID: 34K11
zbMATH DE Number: 1978095
zbMATH Keywords: oscillation theory
author: J. Džurina
author: Ioannis P. Stavroulakis
reviewed by: Jan Ohriska
MaRDI profile type: Publication
cites work: Oscillation criteria for second-order retarded differential equations
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full work available at URL: s0096-3003(02)00243-6
OpenAlex ID: W2126518919
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description: scientific article; zbMATH DE number 1978095