Dependence of the \(n\)th Sturm-Liouville eigenvalue on the problem
type: Item
instance of: scholarly article
title: Dependence of the \(n\)th Sturm-Liouville eigenvalue on the problem
zbMATH Open document ID: 0932.34081
author: Hongyou Wu
author: Anton Zettl
author: Qingkai Kong
published in: Journal of Differential Equations
publication date: 2000-03-06T00:00:00Z
review text: A selfadjoint regular Sturm-Liouville problem with positive leading coefficient and weight function, i.e. \( -(py')'+q(x)y=\lambda\text{wy}\), \(x\in(a,b)\), \[ (A|B)\left(\begin{matrix} y(a)\\ (py')(a)\\ y(b) \\ (py')(b)\end{matrix} \right)=0 \] is considered. Here, \((A|B)\) stands for the set of \((2\times 4)\)-matrices over \(\mathbb{C}\) with rank 2. It was shown by \textit{W. N. Everitt, M. Möller} and \textit{A. Zettl} [in: C. Bandle (ed.) et al., General inequalities 7. Proceedings. Basel: Birkhäuser. ISNM 123, 145-150 (1997; Zbl 0886.34023)] that in general the eigenvalues of the problem do not depend on the problem continuously. In particular, the lowest eigenvalue has an infinite jump when the Sturm-Liouville equation is fixed and the boundary conditions of the problem approach the Dirichlet boundary conditions in a certain way. The authors study the discontinuity set for an eigenvalue of the problem.
reviewed by: V. Pivovarchik
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 1339373
zbMATH Keywords: Sturm-Liouville equation
zbMATH Keywords: eigenvalues
zbMATH Keywords: Dirichlet boundary conditions
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3613
OpenAlex ID: W1984265654
cites work: Algorithm 810: The SLEIGN2 Sturm-Liouville Code
cites work: Automatic Solution of the Sturm-Liouville Problem
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cites work: Dependence of eigenvalues of Sturm-Liouville problems on the boundary
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cites work: Q3123128
cites work: Spectral theory of ordinary differential operators
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DOI: 10.1006/JDEQ.1998.3613
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description: scientific article; zbMATH DE number 1339373