Existence and global stability of positive periodic solution in a logistic integrodifferential equation with feedback control
type: Item
instance of: scholarly article
zbMATH Open document ID: 0981.45003
publication date: 2002-03-03T00:00:00Z
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45M10
Mathematics Subject Classification ID: 45M15
Mathematics Subject Classification ID: 45M20
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47A60
zbMATH DE Number: 1620077
zbMATH Keywords: nonlinear integro-differential equations
zbMATH Keywords: positive periodic solution
zbMATH Keywords: global stability
zbMATH Keywords: feedback control
zbMATH Keywords: continuation theorem
zbMATH Keywords: Lyapunov functional
zbMATH Keywords: system
author: Peixuan Weng
MaRDI profile type: Publication
title: Existence and global stability of positive periodic solution in a logistic integrodifferential equation with feedback control
published in: Annals of Differential Equations
review text: The paper deals with a system of two nonlinear integro-differential equations of first order. Such a construction belongs to the so-called logistic equations, in this connection see the books by \textit{R. E. Gaines} and \textit{J. L. Mawhin} [Coincidence degree and nonlinear differential equations (1977; Zbl 0339.47031)] and by \textit{Y. Kuang} [Delay differential equations with applications in population dynamics (1993; Zbl 0777.34002)]. Logistic equations describe the temporal evolution of a single species of population in a constant environment. Sufficient conditions are given for the existence of at least one positive periodic solution for the system under consideration and for the global asymptotic stability of such a solution. NEWLINENEWLINENEWLINEThe proofs of these results are based on the continuation theorem for the existence of at least one solution of the operator equation with Fredholm operator of index zero (in this connection see the above book by R. E. Gaines and J. L. Mawhin) and on the Lyapunov functional, respectively.
reviewed by: A. A. Kilbas
description: scientific article; zbMATH DE number 1620077