Monotone positive solutions for a fourth order equation with nonlinear boundary conditions
type: Item
instance of: scholarly article
title: Monotone positive solutions for a fourth order equation with nonlinear boundary conditions
zbMATH Open document ID: 1177.34030
author: Edson Alves
author: Maurício Luciano Pelicer
author: To Fu Ma
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-07-10T00:00:00Z
review text: Consider the boundary value problems \[ u^{(4)}(t)=f(t,u,u'),\;0<t<1,\tag{1} \] \[ u(0)=u'(0)=0,\;u'''(1)=g(u(1)),\tag{2} \] \[ u''(1)=0, \tag{3} \] \[ u'(1)=0\tag{4} \] describing bending equilibra of elastic beams. Using the method of lower and upper solutions coupled with monotone iteration, the authors derive conditions on the functions \(f\) and \(g\) such that the boundary value problems \((1),(2),(3)\) and \((1),(2),(4)\) have monotone positive solutions. They also present numerical simulations of the problem \((1),(2),(3)\).
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 5577450
zbMATH Keywords: beam equation
zbMATH Keywords: nonlinear boundary
zbMATH Keywords: monotone iteration
zbMATH Keywords: numerical simulation
zbMATH Keywords: sub and super solutions
MaRDI profile type: Publication
full work available at URL: j.na.2009.02.051
OpenAlex ID: W2031373982
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DOI: 10.1016/J.NA.2009.02.051
description: scientific article; zbMATH DE number 5577450