Periodic solutions of functional differential equations of neutral type
type: Item
instance of: scholarly article
title: Periodic solutions of functional differential equations of neutral type
zbMATH Open document ID: 0876.34075
author: O. Diekmann
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-10-29T00:00:00Z
review text: The paper deals with neutral functional differential equations of the form \[ d/dt\left[x(t)-G(t,x_t)\right] =F(t,x_t),\tag{1} \] where \(F\) and \(G\) are continuous and \(T\) periodic in \(t\). Moreover for all \(r>0\) there exists a real function \(W\) defined on \(\mathbb{R}^+\), \(\lim_{b\to 0^+}W(b)=0\), such that \(|G(t,x_t)-G(s,x_s)|\leq W|t-s|\) for all continuous functions \(x\), \(\sup_{t\in [-h,\infty)}|x(t)|\leq r\), \(t,s\in \mathbb{R}\). (1) is said to be convex, if for all solutions of (1), \(x,y\), \(\alpha x+(1-\alpha)y\) is also a solution of (1) for \(\alpha \in [0,1]\). Necessary and sufficient conditions for the existence of periodic solutions of (1) with finite or infinite delay are given.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 1005607
zbMATH Keywords: functional differential equations of neutral type
zbMATH Keywords: finite and infinite delay
zbMATH Keywords: periodic solutions
reviewed by: Alexandra Rodkina
MaRDI profile type: Publication
OpenAlex ID: W2056982942
DOI: 10.1006/JMAA.1996.0475
description: scientific article; zbMATH DE number 1005607