Existence and uniqueness of periodic solutions for a delay differential equation with piecewise constant arguments
type: Item
instance of: scholarly article
title: Existence and uniqueness of periodic solutions for a delay differential equation with piecewise constant arguments
zbMATH Open document ID: 1167.34031
DOI: 10.4171/PM/1827
author: Haihua Liang
author: Gen-Qiang Wang
published in: Portugaliae Mathematica. Nova Série
publication date: 2009-03-30T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: The aim of this paper is to establish sufficient conditions for the existence and uniqueness of \(T\)-periodic solution of the following delay differential equation with piecewise constant argument: \[ \dot{x}(t)+f(t,x(t-h),x([t-k]))=0, \] where \(h\) and \(k\) are integers, \([\cdot]\) denotes the greatest-integer function, \(f\in C(\mathbb{R}^3;\mathbb{R})\), and \(f(t+T,u,v)=f(t,u,v)\) for \((t,u,v)\in \mathbb{R}^3\). The main tool is Mawhin's continuation theorem. However, the main result is independent of the two delays and the fact of piecewise constant arguments.
reviewed by: Shangjiang Guo
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5535146
zbMATH Keywords: differential equation
zbMATH Keywords: piecewise constant arguments
zbMATH Keywords: periodic solutions
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: Mawhin's continuation theorem
Wikidata QID: Q115211956
MaRDI profile type: Publication
cites work: Oscillatory and Periodic Solutions of Delay Differential Equations with Piecewise Constant Argument
cites work: Q3657815
cites work: A nonlinear equation with piecewise continuous argument
cites work: Retarded differential equations with piecewise constant delays
cites work: An Equation Alternately of Retarded and Advanced Type
cites work: Q3975198
cites work: Coincidence degree, and nonlinear differential equations
cites work: On a logistic equation with piecewise constant arguments
cites work: Oscillations and asymptotic stability of solutions of first order neutral differential equations with piecewise constant argument
cites work: Oscillatory and asymptotic behaviour of first order nonlinear differential equations with retarded argument \([t]\)
cites work: Existence theorem of periodic solutions for a delay nonlinear differential equation with piecewise constant arguments
cites work: Q4463306
description: scientific article; zbMATH DE number 5535146