The method of lower and upper solutions for fourth-order two-point boundary value problems
type: Item
instance of: scholarly article
title: The method of lower and upper solutions for fourth-order two-point boundary value problems
zbMATH Open document ID: 0892.34009
author: Shengmao Fu
author: Ruyun Ma
author: Jihui Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-07-05T00:00:00Z
review text: The method of upper and lower solutions coupled with the monotone iterative technique is used to guarantee the existence of a couple of monotone sequences converging to the extremal solutions in a sector of the following fourth-order boundary value problem: \[ u^{(IV)}(x)=f(x,u(x),u''(x)), \qquad u(0)=u(1)=u''(0)=u''(1)=0, \] where \(f:[0,1]\times \mathbb{R}^{2}\rightarrow \mathbb{R}\) is continuous. In order to demonstrate the main result, the existence of a lower solution \(\beta\) and an upper solution \(\alpha\) with \(\beta\leq\alpha\) and \(\beta''\geq\alpha''\) on \([0,1]\) is assumed. As a previous result, the authors also prove a maximum principle.
reviewed by: Eduardo Liz
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B27
zbMATH DE Number: 1115423
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: monotone method
zbMATH Keywords: maximum principle
zbMATH Keywords: Green functions
MaRDI profile type: Publication
OpenAlex ID: W1975098108
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DOI: 10.1006/JMAA.1997.5639
description: scientific article; zbMATH DE number 1115423