A new angle on Sturm-Liouville problems
type: Item
instance of: scholarly article
title: A new angle on Sturm-Liouville problems
zbMATH Open document ID: 0831.34035
published in: Rocky Mountain Journal of Mathematics
publication date: 1995-09-17T00:00:00Z
review text: In this note Sturm Liouville problems \(- (py')' + qy = \lambda ry\), where \(p > 0\), \(r > 0\), \({1 \over p}, q,r \in L_1 ([0,1], \mathbb{R})\), with boundary conditions \(y(0) \cos \beta_0 = (py') (0) \sin \beta_0\), \(0 \leq \beta_0 < \pi\), \((a \lambda + b) y(0) = (c \lambda + d) (py') (0)\), where \(0 \neq (a,b,c,d) \in \mathbb{R}^4\), are considered. For the three cases (I) \(c = 0 \neq d\), \(e \geq 0\), (II) \(c \neq 0\), \(e > 0\), (III) \(c \neq 0\), \(e < 0\), a Sturm theory is presented. The results are oscillation theorems, asymptotics for the eigenvalues and monotonicity (continuity) of the eigenvalues with respect to a parameter \(t\) upon which \(- \beta_0\), \(- bd,p\) and \(q\) depend monotonically (continuously).
reviewed by: Christiane Tretter
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L20
zbMATH DE Number: 796906
zbMATH Keywords: Sturm Liouville problems
zbMATH Keywords: Sturm theory
zbMATH Keywords: oscillation theorems
zbMATH Keywords: asymptotics for the eigenvalues
zbMATH Keywords: monotonicity
author: P. A. Binding
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072267
OpenAlex ID: W2086608806
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DOI: 10.1216/RMJM/1181072267
description: scientific article; zbMATH DE number 796906