A second-order delay differential equation with multiple periodic solutions
type: Item
instance of: scholarly article
title: A second-order delay differential equation with multiple periodic solutions
zbMATH Open document ID: 0920.34060
author: Joseph Wiener
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-09-23T00:00:00Z
review text: The author considers the equation \[ x''(t)+ \omega^2x(t)= bx([t-1]),\tag{1} \] \(\omega\), \(b\) are real constants, \(b\neq 0\), \([\cdot]\) signifies the greatest integer function. The equation (1) is a differential equation with piecewise constant arguments and represents a hybrid of continuous and discrete dynamical systems. An existence of solutions to (1) is proved. It is shown that for certain values of the coefficieints, some or all of the solutions to (1) are monotone although the corresponding homogeneous equation is clearly oscillatory. For a specific relation between \(\omega\) and \(b\), there exist periodic solutions with different periods.
reviewed by: Alexandra Rodkina
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1251437
zbMATH Keywords: delay differential equations
zbMATH Keywords: periodic solutions
zbMATH Keywords: stability
Wikidata QID: Q115395394
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6196
OpenAlex ID: W2074068542
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DOI: 10.1006/JMAA.1998.6196
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description: scientific article; zbMATH DE number 1251437