Positive solutions of iterative functional differential equations and application to mixed-type functional differential equations
type: Item
instance of: scholarly article
title: Positive solutions of iterative functional differential equations and application to mixed-type functional differential equations
author: Jun Zhou
author: Jun Shen
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2022-10-25T00:00:00Z
review text: In this paper, the authors state some results on the global existence, uniqueness, boundedness and continuous dependence on initial data of positive solutions of a general iterative functional differential equation \[ \dot x(t) = f (t, x(t), x^{[2]}(t), \dots, x^{[n]}(t)), \] where \(f : \mathbb{R}^{n+1}\to \mathbb{R}\) is a nonlinear function and \(x^{[n]}(t)\) represents the \(n\)-th order iteration of \(x(t)\), i.e. \((x^{[n]} (t) = x(x^{[n-1]}(t))\) for all \(n\in\mathbb{N}\) and \(x^{[0]}(t) = t\). To achieve their goal, they use Krasnoselskii fixed point theorem.
reviewed by: Mustapha Yebdri
Mathematics Subject Classification ID: 34K43
Mathematics Subject Classification ID: 34K12
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7606611
zbMATH Keywords: iterative functional differential equations
zbMATH Keywords: state-dependence
zbMATH Keywords: positive solutions
zbMATH Keywords: functional inequality
zbMATH Keywords: integral inequality
zbMATH Keywords: Krasnoselskii fixed point theorem
Wikidata QID: Q115219179
MaRDI profile type: Publication
full work available at URL: dcdsb.2021198
OpenAlex ID: W3187354046
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DOI: 10.3934/DCDSB.2021198
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description: scientific article; zbMATH DE number 7606611