Asymptotic periodicity, monotonicity, and oscillation of solutions of scalar neutral functional differential equations
type: Item
instance of: scholarly article
title: Asymptotic periodicity, monotonicity, and oscillation of solutions of scalar neutral functional differential equations
zbMATH Open document ID: 0855.34087
author: Jianhong Wu
author: Tibor Krisztin
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-07-14T00:00:00Z
review text: Periodic solutions to the scalar neutral functional-differential equation (1) \(d/dt [x(t) - c(t) x(t - s)] = - h(t, x(t)) + h(t - s, x(t - s))\) are considered. Both \(c\) and \(h\) are 1-periodic, \(h\) is increasing in \(x\). It is shown that the set of 1-periodic solutions is an ordered arc and each solution is convergent to a periodic solution. The asymptotic behavior of each solution is classified in terms of the value of the first integral at the initial condition. A wide description of earlier results connected with special cases of (1) is considered.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 902558
zbMATH Keywords: periodic solution
zbMATH Keywords: scalar neutral functional-differential equation
reviewed by: Tadeusz Dłotko
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0158
OpenAlex ID: W2059507929
DOI: 10.1006/JMAA.1996.0158
description: scientific article; zbMATH DE number 902558