Existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions
type: Item
instance of: scholarly article
title: Existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions
zbMATH Open document ID: 0958.34055
DOI: 10.1016/S0898-1221(00)00171-1
publication date: 2000-11-13T00:00:00Z
review text: Consider the periodic boundary value problem \[ du(t)/dt =g(t,u(t), u(\Theta(t))), \;u (0)=u(T), \;0 \leq t \leq T,\tag{*} \] where \(g:[0,T] \times \mathbb{R}^2 \rightarrow \mathbb{R}\) and \(\Theta: [0,T] \rightarrow \mathbb{R}\) are continuous, \(0 \leq \Theta (t) \leq t.\) First, the authors study the linear problem \(du(t)/dt+M u(t) +Nu(\Theta (t)) = \sigma (t)\) with \(\sigma \in C([0,T], \mathbb{R})\) and prove maximum principles for different boundary inequality conditions. Using these principles, the authors define upper and lower solutions to \((*)\) and derive conditions such that the existence of ordered lower and upper solutions imply the existence of a solution to \((*)\). Finally, a result for monotone iteration is proved.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K07
Mathematics Subject Classification ID: 34K05
zbMATH DE Number: 1528536
zbMATH Keywords: functional-differential equation
zbMATH Keywords: periodic boundary value problem
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: monotone iterative method
Wikidata QID: Q60199467
author: Juan J. Nieto
author: Rosana Rodrıǵuez-López
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
cites work: Q3807603
cites work: Periodic boundary value problems for nonlinear first order ordinary differential equations
cites work: Remarks on the periodic boundary value problems for first-order differential equations
cites work: Periodic boundary value problems for a class of functional differential equations
full work available at URL: s0898-1221(00)00171-1
OpenAlex ID: W2074718318
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1528536