The method of lower and upper solutions for a bending of an elastic beam equation
type: Item
instance of: scholarly article
title: The method of lower and upper solutions for a bending of an elastic beam equation
zbMATH Open document ID: 1016.34010
author: Zhanbing Bai
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-09-14T00:00:00Z
review text: The author considers the fourth-order nonlinear boundary value problem \[ u^{(4)}(x)= f(x, u(x), u''(x)),\quad 0< x< 1,\quad u(0)= u(1)= u''(0)= u''(1)= 0. \] An appropriate maximum principle for the linear case is obtained and used to prove the existence of monotone sequences of functions that converge to solutions to the nonlinear problem. It is assumed that \(f(x,u,v)\) is continuous and satisfies some inequalities, which can be considered as a relaxation of monotonicity in \(u\), \(v\). No growth restrictions are imposed on \(f\). An example is given.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 1506528
zbMATH Keywords: existence
zbMATH Keywords: solutions
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: maximum principle
reviewed by: Sergei A. Brykalov
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6887
OpenAlex ID: W1964681504
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DOI: 10.1006/JMAA.2000.6887
description: scientific article; zbMATH DE number 1506528