On the asymptotic behavior of some nonlinear delay differential systems
type: Item
instance of: scholarly article
zbMATH Open document ID: 0995.34074
author: Serena Matucci
publication date: 2002-10-15T00:00:00Z
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 1672652
zbMATH Keywords: third-order delay differential equations
zbMATH Keywords: existence of solutions
zbMATH Keywords: extinction
MaRDI profile type: Publication
title: On the asymptotic behavior of some nonlinear delay differential systems
published in: Dynamics of Continuous, Discrete \& Impulsive Systems. Series A. Mathematical Analysis
review text: Here, the author first investigates the existence of solutions for delay differential equations. The approach used to prove existence results is relatively original. The idea is to consider the delay terms as forcing terms for an ordinary differential equation. The second part of the paper is concerned with the convergence of the solutions to zero (which is an equilibrium) for \(t\to\infty\). In this second part, the author does not apply the existence results obtained in the first part, some known results for the example under consideration are exploited. Then by using global stability results for nonautonomous perturbations of a linear scalar ordinary differential equation, and some estimations, the author proves the convergence of positive solutions to zero.
reviewed by: Pierre Magal
description: scientific article; zbMATH DE number 1672652