Multiple positive periodic solutions of nonlinear functional differential system with feedback control.
type: Item
instance of: scholarly article
title: Multiple positive periodic solutions of nonlinear functional differential system with feedback control.
zbMATH Open document ID: 1045.34045
author: Ping Liu
author: Yongkun Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-01-26T00:00:00Z
review text: The paper deals with a two-dimensional nonautonomous system of functional-differential equations of a special form. Namely, it is assumed that each equation consists of the main part (linear in the state variable) and the feedback control that is a nonlinear function containing the delayed links. The basic results of the work are the theorems 1 and 2 giving sufficient conditions for the existence of at least two positive \(\omega\)-periodic solutions of the considered system. The proofs of the theorems are based on a generalization of the well-known fixed-point theorem of Leggett-Williams.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 93B52
zbMATH DE Number: 2032945
zbMATH Keywords: positive periodic solution
zbMATH Keywords: functional-differential equation, feedback control
reviewed by: Vyacheslav I. Maksimov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.09.055
OpenAlex ID: W2086726272
cites work: Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics.
cites work: Oscillation and global attractivity in a periodic Nicholson's blowflies model
cites work: Q4544904
cites work: Global attractivity and oscillation in a nonlinear delay equation
cites work: Q5509221
cites work: Delay differential equations: with applications in population dynamics
cites work: Positive periodic solutions of a class of delay differential system with feedback control.
cites work: Coincidence degree, and nonlinear differential equations
cites work: Existence and global stability of positive periodic solution of periodic integro-differential systems with feedback controls
cites work: Existence and global attractivity of positive periodic solutions to a logistic growth system with feedback control and deviating arguments
cites work: Feedback regulation of logistic growth
cites work: Q3854213
cites work: Two positive fixed points of nonlinear operators on ordered Banach spaces
cites work: Q3996430
DOI: 10.1016/J.JMAA.2003.09.055
description: scientific article; zbMATH DE number 2032945