On the asymptotic behavior of the solutions of a class of scalar neutral equations generating a monotone semi-flow
type: Item
instance of: scholarly article
title: On the asymptotic behavior of the solutions of a class of scalar neutral equations generating a monotone semi-flow
zbMATH Open document ID: 0711.34097
DOI: 10.1016/0022-0396(90)90017-J
author: F. Bourad
author: Ovide Arino
published in: Journal of Differential Equations
publication date: 1990-01-01T00:00:00Z
review text: Consider the scalar neutral type equation \[ (1)\quad \frac{d}{dt}\{x(t)- cx(t-1)\}=f(t-1,x(t-1))-f(t,x(t)), \] where f is increasing in x and \(0<c<1\). Using the theory of monotone semi-flows which have a monotone first integral, the authors show that the asymptotic behaviour of bounded solutions depends only on the value of a first integral of (1). If f(t,x) is an almost periodic or periodic function, or even constancy in time, then the positively bounded solutions share asymptotically the same properties. The autonomous and nonautonomous cases, where all the solutions are bounded are also considered.
reviewed by: C.Simirad
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 4169166
zbMATH Keywords: scalar neutral type equation
zbMATH Keywords: monotone semi-flows
zbMATH Keywords: asymptotic behaviour of bounded solutions
MaRDI profile type: Publication
cites work: Q3796439
cites work: Q3943278
cites work: Monotone semiflows generated by functional differential equations
full work available at URL: 0022-0396(90)90017-j
OpenAlex ID: W1998244583
description: scientific article; zbMATH DE number 4169166