The periodic solutions of nonlinear differential difference equations
type: Item
instance of: scholarly article
title: The periodic solutions of nonlinear differential difference equations
zbMATH Open document ID: 0806.34061
author: Yongshao Chen
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-09-08T00:00:00Z
review text: The existence of slowly oscillating periodic solutions and rapidly oscillating solutions to a class of differential difference equations is considered. Sufficient conditions under which the equations have at least \(N\) or an infinite number of nonconstant periodic solutions are established. For example, it is shown that if \(ah > {\pi \over 2}\), then the equation \(x'(t) = - x(t - h) (a - bx^ 2(t) - cx^ 2 (t - h))\), \(h>0\), \(a>0\), \(b \geq 0\), \(c \geq 0\), \(b^ 2 + c^ 2 \neq 0\) has a nonconstant periodic solution with period of \(4h/1 + 4n\), \(n = 0,1, \dots, N - 1\), where \(N\) is the greatest integer which is less than \(ah - {3 \over 2} \pi/2 \pi\).
Mathematics Subject Classification ID: 34K99
zbMATH DE Number: 635934
zbMATH Keywords: slowly oscillating periodic solutions
zbMATH Keywords: rapidly oscillating solutions
zbMATH Keywords: differential difference equations
reviewed by: Izabela Foltyńska
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1210
OpenAlex ID: W2068616823
DOI: 10.1006/JMAA.1994.1210
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description: scientific article; zbMATH DE number 635934