A cantilever beam problem with small deflections and perturbed boundary data
type: Item
instance of: scholarly article
title: A cantilever beam problem with small deflections and perturbed boundary data
zbMATH Open document ID: 1487.34068
DOI: 10.1155/2021/9081623
author: Ammar Khanfer
author: Lazhar Bougoffa
published in: Journal of Function Spaces
publication date: 2021-12-16T00:00:00Z
review text: In this paper, the authors study the cantilever beam problem modeled by a fourth order nonlinear differential equation subject to integral boundary conditions of the form \[ \begin{cases} u^{(4)}(x)=\lambda f\Big(x, u(x), u'(x), u''(x), u'''(x)\Big)=0, \quad 0\leq x\leq 1,\\ u(0)=u'(0)=\int_0^1p(x)u(x)dx,~ u''(1)=u'''(1)=\int_0^1q(x)u''(x)dx, \end{cases} \] where \(f\) is continuous on \([0,1]\times [0,\infty)\times [0,\infty)\times (-\infty,0]\times (-\infty,0]\) and \(p,q\in L^1[0,1].\) An existence theorem is established via Schauder's fixed point theorem, which implies that small deflections continue to exist on the beam whether it is perfectly cantilevered or not.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7446746
zbMATH Keywords: fully fourth order nonlinear boundary value problem
zbMATH Keywords: integral boundary conditions
zbMATH Keywords: existence of solution
zbMATH Keywords: cantilever beam equation
zbMATH Keywords: Schauder fixed point theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/9081623
OpenAlex ID: W3212642271
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description: scientific article; zbMATH DE number 7446746