On the maximum and minimum of some functionals for the eigenvalue problem of Sturm-Liouville type
type: Item
instance of: scholarly article
title: On the maximum and minimum of some functionals for the eigenvalue problem of Sturm-Liouville type
zbMATH Open document ID: 0796.34020
published in: Journal of Differential Equations
publication date: 1994-03-24T00:00:00Z
review text: One considers the eigenvalues \(\lambda_ n= \lambda_ n(q)\) of the Sturm-Liouville equation \(y''+ (\lambda- q(x))y= 0\), with the boundary conditions \(y(-\ell)= y(\ell)=0\). Let \(E(h,H,M,\ell)\) be the set of potential functions \(q\) such that \(h\leq q(x)\leq H\), \(\int^ \ell_ \ell q(x)dx= M\). One determines the potential functions in \(E(h,H,M,\ell)\) which extremize \(\lambda_ n(q)\) and minimize \(\lambda_ 2(q)- \lambda_ 1(q)\).
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 522668
zbMATH Keywords: eigenvalues
zbMATH Keywords: Sturm-Liouville equation
zbMATH Keywords: potential functions
author: Hua-Huai Chern
author: Chao-Liang Shen
reviewed by: Jacques Faraut
MaRDI profile type: Publication
full work available at URL: jdeq.1994.1003
OpenAlex ID: W1988563347
DOI: 10.1006/JDEQ.1994.1003
description: scientific article; zbMATH DE number 522668