Oscillations in integrodifferential equations of arbitrary order
type: Item
instance of: scholarly article
title: Oscillations in integrodifferential equations of arbitrary order
zbMATH Open document ID: 0632.45002
DOI: 10.1016/0022-247X(87)90078-3
author: K. Gopalsamy
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The author gives sufficient conditions for all bounded solutions of a class of scalar linear integrodifferential equations of nth order on \((0,+\infty)\) (n a positive integer) to be either oscillatory or converge to zero, as \(t\to \infty\). In the case of linear delay-differential equations, the sufficient conditions are also shown to be necessary for all bounded solutions to be oscillatory. By means of a comparison with an appropriate linear equation, similar results are derived for nonlinear integrodifferential and delay-differential equations.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45M05
zbMATH DE Number: 4028114
zbMATH Keywords: oscillatory solution
zbMATH Keywords: bounded solutions
zbMATH Keywords: linear integrodifferential equations
zbMATH Keywords: linear delay-differential equations
zbMATH Keywords: nonlinear
reviewed by: Sergiu Aizicovici
MaRDI profile type: Publication
cites work: Q5728644
cites work: Theory of functional differential equations. 2nd ed
cites work: Q4134269
cites work: Sharp conditions for oscillations caused by delays
cites work: Boundedness and oscillation of some Volterra and delay equations
cites work: Q5849376
description: scientific article; zbMATH DE number 4028114