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A Sturm–Liouville problem depending rationally on the eigenvalue parameter

✍ Scribed by Peter Jonas; Carsten Trunk

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
234 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We consider the Sturm–Liouville problem (1.1) and (1.2) with a potential depending rationally on the eigenvalue parameter. With these equations a λ ‐linear eigenvalue problem is associated in such a way that L~2~‐solutions of (1.1), (1.2) correspond to eigenvectors of a linear operator. If the functions q and u are real and satisfy some additional conditions, the corresponding linear operator is a definitizable self‐adjoint operator in some Krein space. Moreover we consider the problem (1.1) and (1.3) on the positive half‐axis. Here we use results on the absense of positive eigenvalues for Sturm–Liouville operators to exclude critical points of the associated definitizable operator. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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