Remarks on the periodic boundary value problems for first-order differential equations
type: Item
instance of: scholarly article
title: Remarks on the periodic boundary value problems for first-order differential equations
zbMATH Open document ID: 0936.34013
DOI: 10.1016/S0898-1221(99)00100-5
author: Zhuang Wan
author: Yubo Chen
author: Jie Chen
publication date: 2000-05-08T00:00:00Z
review text: The authors apply the method of upper and lower solutions and the monotone iterative technique to the first-order periodic boundary value problem \(u'(t)=f(t,u(t))\), \(t\in I=[0,2\pi]\); \(u(0)=u(2\pi)\), where \(f:I\times \mathbb{R}\to \mathbb{R}\) is a continuous function. They investigate the case when the classical inequalities for the boundary conditions are violated in the definitions of the upper and lower solutions. Some examples are included showing the applicability of the main results and the necessity of requiring new hypotheses on the nonlinearity \(f\).
reviewed by: Eduardo Liz
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 1357964
zbMATH Keywords: periodic boundary value problems
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: monotone iterative technique
MaRDI profile type: Publication
cites work: Existence and monotone method for periodic solutions of first-order differential equations
cites work: Remarks on first and second order periodic boundary value problems
cites work: Periodic boundary value problems of first and second order differential equations
cites work: Q3807603
cites work: An Abstract Existence Theorem at Resonance
cites work: Q5185568
full work available at URL: s0898-1221(99)00100-5
OpenAlex ID: W2021134447
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1357964