Periodic solutions of a second-order functional differential equation with state-dependent argument
type: Item
instance of: scholarly article
title: Periodic solutions of a second-order functional differential equation with state-dependent argument
zbMATH Open document ID: 1408.34050
author: Hou Yu Zhao
author: Jia Liu
published in: Mediterranean Journal of Mathematics
publication date: 2018-12-28T00:00:00Z
review text: In this paper, a second order functional differential equation with state-dependent argument is considered: \[ c_0x''(t)+c_1x'(t) +c_2x(t) = x(p(t)+bx(t))+h(t), \] where \(c_i\) and \(b\) are nonzero constants and \(p\) and \(h\) are periodic functions with period \(T>0\). Under suitable assumptions and by using Schauder and Banach fixed point theorems, existence and uniqueness of a periodic solution is proved and continuous dependence of the periodic solution on \(p\) and \(h\) is shown to be valid.
reviewed by: Zhanyuan Hou
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6997091
zbMATH Keywords: functional differential equations
zbMATH Keywords: state-dependent argument
zbMATH Keywords: periodic solution
zbMATH Keywords: fixed point theorem
Wikidata QID: Q115390320
MaRDI profile type: Publication
full work available at URL: s00009-018-1261-2
OpenAlex ID: W2899727175
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DOI: 10.1007/S00009-018-1261-2
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description: scientific article; zbMATH DE number 6997091