Using time scales to study multi-interval Sturm-Liouville problems with interface conditions
type: Item
instance of: scholarly article
title: Using time scales to study multi-interval Sturm-Liouville problems with interface conditions
zbMATH Open document ID: 1263.34032
published in: Results in Mathematics
publication date: 2013-02-08T00:00:00Z
review text: The authors consider a Sturm-Liouville problem defined on multiple intervals with interface conditions. The existence of a sequence of eigenvalues is established and the zero counts of the associated eigenfunctions are determined. Moreover, the authors reveal the continuous and discontinuous nature of the eigenvalues on the boundary condition. The approach in this paper is different from those in the literature. The authors transfer the Sturm-Liouville problem with interface conditions to a Sturm-Liouville problem on a time scale without interface conditions and then apply the Sturm-Liouville theory for equations on time scales. In this way, the authors are able to investigate the problem from a global point of view. Consequently, the authors results cover the cases when the potential function in the equation is not strictly greater than zero and when the domain consists of an infinite number of intervals.
reviewed by: Bilender P. Allahverdiev
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 6135258
zbMATH Keywords: multi-interval Sturm-Liouville problems
zbMATH Keywords: interface conditions
zbMATH Keywords: time scales
zbMATH Keywords: existence of eigenvalues
zbMATH Keywords: dependence on the problem
author: Qingkai Kong
author: Qiru Wang
MaRDI profile type: Publication
full work available at URL: s00025-011-0208-8
OpenAlex ID: W2129122268
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DOI: 10.1007/S00025-011-0208-8
description: scientific article; zbMATH DE number 6135258