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A hierarchy of Sturm–Liouville problems

✍ Scribed by Paul Binding

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
86 KB
Volume
26
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

Sturm–Liouville equations will be considered where the boundary conditions depend rationally on the eigenvalue parameter. Such problems apply to a variety of engineering situations, for example to the stability of rotating axles. Classesof these problems will be isolated with a rather rich spectral structure, for example oscillation, comparison and completeness properties analogous to thoseof the ‘usual’ Sturm–Liouville problem which has constant boundary conditions.In fact it will be shown how these classes can be converted into each other, andinto the ‘usual’ Sturm–Liouville problem, by means of transformations preserving all but finitely many eigenvalues. Copyright © 2003 John Wiley & Sons, Ltd.

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