Bernstein approximations of nonlinear Sturm-Liouville problems
type: Item
instance of: scholarly article
title: Bernstein approximations of nonlinear Sturm-Liouville problems
zbMATH Open document ID: 1200.34027
author: Jacek Gulgowski
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-02-12T00:00:00Z
review text: This is an interesting article that deals with the Sturm-Liouville boundary value problem \[ u''(t)+\phi(t,u(t),u'(t),\lambda)=0,\quad t\in(0,1) \] with boundary conditions \(L(u)=0\). This may include nonlinear boundary value problems for some classes of ordinary differential equations. The main idea is to approximate these differential equations by finite dimensional Bernstein approximations given explicitely in the paper. The author uses a global bifurcation theorem to obtain existence results for nonlinear Sturm-Liouville problems. The paper, overall, interesting and useful, however, it is more suitable for specialists.
reviewed by: Nasser Saad
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 41A99
zbMATH DE Number: 5669288
zbMATH Keywords: Sturm-Liouville problem
zbMATH Keywords: Bernstein polynomial
zbMATH Keywords: global bifurcation
MaRDI profile type: Publication
full work available at URL: j.na.2009.11.040
OpenAlex ID: W2052369751
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DOI: 10.1016/J.NA.2009.11.040
description: scientific article; zbMATH DE number 5669288