An iterative method for functional differential equations
type: Item
instance of: scholarly article
title: An iterative method for functional differential equations
zbMATH Open document ID: 1071.34064
author: Mustapha Yebdri
author: Sidi Mohamed Bouguima
author: Ovide Arino
published in: Applied Mathematics and Computation
publication date: 2005-02-22T00:00:00Z
review text: The authors consider the problem \[ \dot x(t)=f(t,x(t),x_t),\quad x_0(\theta)=x_{2\pi}(\theta),\quad \theta\in [-r,0], \] where \(f\colon I\times \mathbb{R}\times C\to C\) is a continuous function, \(I=[0,2\pi]\) and \(C=C([-r,0],\mathbb{R})\) is the space of continuous real-valued functions defined on \([-r,0]\). The set \(C\) is a Banach space with supremum norm. Upper and lower functions for this problem are defined and are used for the construction of a monotone iterative method to prove the existence of a solution of the problem considered. As application, the special case \( f(t,x(t),x_t):=g(t,x_t)-Kx(t)\) with \(g\) continuous and positive constant \(K\) is considered for which the existence of at least one solution of the periodic boundary problem is proved.
reviewed by: Josef Diblík
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34K13
zbMATH DE Number: 2136142
zbMATH Keywords: functional-differential equation
zbMATH Keywords: periodic boundary conditions
zbMATH Keywords: iterative method
zbMATH Keywords: lower and upper solutions
MaRDI profile type: Publication
full work available at URL: j.amc.2003.12.026
OpenAlex ID: W2025773441
cites work: Periodic boundary value problems and monotone iterative methods for functional differential equations
cites work: Q3807603
cites work: Periodic boundary value problem for differential equations with delay and monotone iterative method
cites work: Periodic boundary value problems for a class of functional differential equations
DOI: 10.1016/J.AMC.2003.12.026
description: scientific article; zbMATH DE number 2136142