When all solutions of \(x'=-\Sigma q_ i(t)x(t-T_ i(t))\) oscillate
type: Item
instance of: scholarly article
title: When all solutions of \(x'=-\Sigma q_ i(t)x(t-T_ i(t))\) oscillate
zbMATH Open document ID: 0571.34057
DOI: 10.1016/0022-0396(84)90036-6
author: Brian R. Hunt
author: James A. Yorke
published in: Journal of Differential Equations
publication date: 1984-01-01T00:00:00Z
review text: This paper generalizes some results of \textit{G. Ladas, Y. G. Sficas} and \textit{I. P. Stavroulakis} concerning oscillatory solutions of the delay equation \(x'(t)=-\sum^{n}_{i=1}q_ ix(t-T_ i)\) [cf. Am. Math. Mon. 90, 637-640 (1983; Zbl 0526.34054)]. This paper considers delay equations of the form \(x'(t)=-\sum^{n}_{i=1}q_ i(t)x(t-T_ i(t))\) where \(T_ i\) and \(q_ i\) are continuous, positive functions on [0,\(\infty)\). The main result is that if there is a uniform upper bound \(T_ 0\) on the \(T_ i's\) and if the ''total torque'' \(\tau (t)=\sum^{n}_{i=1}q_ i(t)T_ i(t)\) satisfies \(\lim \inf_{t\to \infty} \tau (t)>1/e\) then all solutions of the above differential delay equation must oscillate.
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 3910836
zbMATH Keywords: oscillatory solutions
zbMATH Keywords: delay equation
zbMATH Keywords: total torque
reviewed by: Lawrence M. Perko
MaRDI profile type: Publication
full work available at URL: 0022-0396(84)90036-6
OpenAlex ID: W2065906671
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description: scientific article; zbMATH DE number 3910836