Positive periodic solutions of nonlinear functional differential equations
type: Item
instance of: scholarly article
title: Positive periodic solutions of nonlinear functional differential equations
zbMATH Open document ID: 1084.34061
author: Lifei Zhu
author: Yongkun Li
published in: Applied Mathematics and Computation
publication date: 2004-11-23T00:00:00Z
review text: The authors investigates the existence of positive periodic solutions for the first-order functional-differential equation \[ x'(t)= -a(t) x(t)+ f(t, x_t),\tag{\(*\)} \] where \(a(t)\) is a \(T\)-periodic function satisfying \[ \exp\Biggl(\int^T_0 a(u) du\Biggr)> 1, \] \(f(t, x_t)\) is a nonnegative function defined on \(\mathbb{R}\times BC\), where \(BC\) denotes the Banach space of bounded continuous functions. By using a generalized form of the Leggett-Williams fixed-point theorem, the authors obtain some sufficient conditions for equation \((*)\) to have at least two positive \(T\)-periodic solutions.
reviewed by: He Chungyou
Mathematics Subject Classification ID: 34K13
zbMATH DE Number: 2118019
zbMATH Keywords: Functional-differential equation
zbMATH Keywords: Positive periodic solutions
zbMATH Keywords: Fixed-point theorem
MaRDI profile type: Publication
full work available at URL: j.amc.2003.07.013
OpenAlex ID: W2014537578
cites work: Existence of positive periodic solutions for non-autonomous functional differential equations
cites work: Twin solutions of boundary value problems for ordinary differential equations and finite difference equations
cites work: Q4952140
cites work: Q4544904
DOI: 10.1016/J.AMC.2003.07.013
description: scientific article; zbMATH DE number 2118019