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Subordinacy Analysis and Absolutely Continuous Spectra for Sturm-Liouville Equations with Two Singular Endpoints

Published online by Cambridge University Press:  20 November 2018

Dominic P. Clemence
Dominic P. Clemence*
Affiliation:
Department of Mathematics North Carolina Agricultural and Technical State University Greensboro, NC 27411 USA
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Abstract

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The Gilbert-Pearson characterization of the spectrum is established for a generalized Sturm-Liouville equation with two singular endpoints. It is also shown that strong absolute continuity for the one singular endpoint problem guarantees absolute continuity for the two singular endpoint problem. As a consequence, we obtain the result that strong nonsubordinacy, at one singular endpoint, of a particular solution guarantees the nonexistence of subordinate solutions at both singular endpoints.

Keywords

34L0534B2034B24
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 1 , 01 March 1998 , pp. 23 - 27
Copyright
Copyright © Canadian Mathematical Society 1998

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