Periodic solutions to a kind of neutral functional differential equation in the critical case
type: Item
instance of: scholarly article
title: Periodic solutions to a kind of neutral functional differential equation in the critical case
zbMATH Open document ID: 1057.34096
author: Shiping Lu
author: Weigao Ge
author: Zuxiu Zheng
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
review text: The authors study a kind of first-order neutral functional-differential equation of the form \[ (x(t)- cx(t-\tau))'= g(t,x(t-\mu(t)))+ e(t), \tag{1} \] where \(g\in C(\mathbb{R}\times \mathbb{R}; \mathbb{R})\) with \(g(t+2\pi,x)= g(t,x)\) for all \(x\in \mathbb{R}\), \(e\) and \(\mu\) are continuous periodic functions with period \(2\pi\), and \(c,\tau\in \mathbb{R}\) are two constants. The authors investigate the existence of periodic solutions to (1) in the critical case \(| c|=1\). Using Mawhin's continuation theorem and topological degree theory, the authors obtain some new results on the existence of \(2\pi\)-periodic solutions.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 2082156
zbMATH Keywords: odd periodic solution
zbMATH Keywords: topological degree theory
zbMATH Keywords: Mawhin's continuation theorem
zbMATH Keywords: critical case
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.01.031
OpenAlex ID: W2070764855
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Wikidata QID: Q115346372
DOI: 10.1016/J.JMAA.2004.01.031
description: scientific article; zbMATH DE number 2082156