Linear second-order problems with Sturm-Liouville-type multi-point boundary conditions

We consider the eigenvalue problem for the equation $-u'' = lambda u$ on $(-1,1)$, together with general Sturm-Liouville-type, multi-point boundary conditions at $pm 1$. We show that the basic spectral properties of this problem are similar to those of the standard Sturm-Liouville pro...

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Main Author:	Bryan P. Rynne
Format:	Article
Language:	English
Published:	Texas State University 2012-08-01
Series:	Electronic Journal of Differential Equations
Subjects:	Second order ordinary differential equations multi-point boundary conditions Sturm-Liouville problems
Online Access:	http://ejde.math.txstate.edu/Volumes/2012/146/abstr.html

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spelling	doaj-12024650e6214501971c772d2ec368182020-11-25T00:48:44ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-08-012012146,121Linear second-order problems with Sturm-Liouville-type multi-point boundary conditionsBryan P. RynneWe consider the eigenvalue problem for the equation $-u'' = lambda u$ on $(-1,1)$, together with general Sturm-Liouville-type, multi-point boundary conditions at $pm 1$. We show that the basic spectral properties of this problem are similar to those of the standard Sturm-Liouville problem with separated boundary conditions. In particular, for each integer $k ge 0$ there exists a unique, simple eigenvalue $lambda_k$ whose eigenfunctions have 'oscillation count' equal to k. http://ejde.math.txstate.edu/Volumes/2012/146/abstr.htmlSecond order ordinary differential equationsmulti-point boundary conditionsSturm-Liouville problems
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Bryan P. Rynne
spellingShingle	Bryan P. Rynne Linear second-order problems with Sturm-Liouville-type multi-point boundary conditions Electronic Journal of Differential Equations Second order ordinary differential equations multi-point boundary conditions Sturm-Liouville problems
author_facet	Bryan P. Rynne
author_sort	Bryan P. Rynne
title	Linear second-order problems with Sturm-Liouville-type multi-point boundary conditions
title_short	Linear second-order problems with Sturm-Liouville-type multi-point boundary conditions
title_full	Linear second-order problems with Sturm-Liouville-type multi-point boundary conditions
title_fullStr	Linear second-order problems with Sturm-Liouville-type multi-point boundary conditions
title_full_unstemmed	Linear second-order problems with Sturm-Liouville-type multi-point boundary conditions
title_sort	linear second-order problems with sturm-liouville-type multi-point boundary conditions
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2012-08-01
description	We consider the eigenvalue problem for the equation $-u'' = lambda u$ on $(-1,1)$, together with general Sturm-Liouville-type, multi-point boundary conditions at $pm 1$. We show that the basic spectral properties of this problem are similar to those of the standard Sturm-Liouville problem with separated boundary conditions. In particular, for each integer $k ge 0$ there exists a unique, simple eigenvalue $lambda_k$ whose eigenfunctions have 'oscillation count' equal to k.
topic	Second order ordinary differential equations multi-point boundary conditions Sturm-Liouville problems
url	http://ejde.math.txstate.edu/Volumes/2012/146/abstr.html
work_keys_str_mv	AT bryanprynne linearsecondorderproblemswithsturmliouvilletypemultipointboundaryconditions
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Linear second-order problems with Sturm-Liouville-type multi-point boundary conditions

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