Geometric properties of the self-adjoint Sturm-Liouville problems
type: Item
instance of: scholarly article
title: Geometric properties of the self-adjoint Sturm-Liouville problems
zbMATH Open document ID: 1073.34024
author: Xinhua Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-04-21T00:00:00Z
review text: Considering the (real) quadratic form \[ U=\frac12\int_0^L \left(p(x)(w'(x))^2+q(x)w(x)\right)dx, \] also called energy functional, associated with the selfadjoint Sturm-Liouville problem \[ (pw')'-qw+\lambda \rho w=0,\;0\leq x\leq L,\quad w(0)=w(L)=0, \] the author uses the variational principle to relate curvature lines and curvature of \(z=U\) to eigenvectors and eigenvalues, respectively, of the Sturm-Liouville problem. Hilbert spaces \(H_1\) and \(H_{11}\) occur, but are not defined explicitly. Most likely, they are certain Sobolev spaces with suitable boundary conditions.
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 49R50
zbMATH DE Number: 2159775
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenvector
zbMATH Keywords: variational principle
zbMATH Keywords: curvature
zbMATH Keywords: energy functional
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.10.026
OpenAlex ID: W2078259185
cites work: Q3999241
cites work: Q4142292
cites work: Numerical methods for higher order Sturm-Liouville problems
DOI: 10.1016/J.JMAA.2004.10.026
description: scientific article; zbMATH DE number 2159775