Variable Change for Sturm-Liouville Differential Expression on Time Scales

Abstract

We study second order scalar delta derivative expressions of Sturm-Liouville type on our newly defined Sturmian time scales. Sturmian time scales include the discrete and continuous cases studied by Sturm. A form of second order differential expression on a Sturmian time scale considered here satisfies a Green's identity and hence is"formally self-adjoint”. A unified variable change method is developed which allows simultaneous change of independent and dependent variable for expressions which include continuous and discrete theories as special cases. This unifies a continuous result of Coppel with a discrete result of Voepel. For the fourth order case, we explore unification of a continuous result of Ahlbrandt, Hinton and Lewis [4] with a discrete result of Voepel [32].

Department(s)

Mathematics and Statistics

Keywords and Phrases

Sturm-Liouvill equations; Time scales; Delta derivatives; variable change

International Standard Serial Number (ISSN)

1023-6198

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2003 Taylor & Francis, All rights reserved.

Publication Date

01 Jan 2003

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