Nodal solutions of multi-point boundary value problems
type: Item
instance of: scholarly article
title: Nodal solutions of multi-point boundary value problems
zbMATH Open document ID: 1195.34028
author: Lingju Kong
author: James S. W. Wong
author: Qingkai Kong
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-01-12T00:00:00Z
review text: The authors study a nonlinear multipoint boundary value problem of the form \[ y''+ w(t) f(y)= 0,\qquad t\in (a,b), \] \[ \cos\alpha\;y(\alpha)- \sin\alpha\;y')a_= 0, \] \[ y(b)- \sum^m_{i=1} k_i y(\eta_i)= 0. \] Here \(zf(z)> 0\) for all \(z\neq 0\). The coefficient \(w(t)\) is positive. Sufficient conditions are obtained for the existence and nonexistence of nodal solutions, which have specific properties of zeroes of the solution and its first derivative. These sufficient conditions are formulated with the help of eigenvalues of an auxiliary Sturm-Liouville problem.
reviewed by: Sergei A. Brykalov
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5656718
zbMATH Keywords: nodal solutions
zbMATH Keywords: multi-point boundary value problems
zbMATH Keywords: Sturm-Liouville problems
zbMATH Keywords: eigenvalues
MaRDI profile type: Publication
full work available at URL: j.na.2009.06.072
OpenAlex ID: W2086466404
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DOI: 10.1016/J.NA.2009.06.072
description: scientific article; zbMATH DE number 5656718