Spectral asymptotics for Sturm-Liouville equations with indefinite weight

Authors:
Paul A. Binding, Patrick J. Browne and Bruce A. Watson

Journal:
Trans. Amer. Math. Soc. **354** (2002), 4043-4065

MSC (2000):
Primary 34L20, 34B09, 34B24; Secondary 47E05

DOI:
https://doi.org/10.1090/S0002-9947-02-03023-4

Published electronically:
May 22, 2002

MathSciNet review:
1926864

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The Sturm-Liouville equation

is considered subject to the boundary conditions

We assume that is positive and that is piecewise continuous and changes sign at its discontinuities. We give asymptotic approximations up to for , or equivalently up to for , the eigenvalues of the above boundary value problem.

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Additional Information

**Paul A. Binding**

Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4

Email:
binding@ucalgary.ca

**Patrick J. Browne**

Affiliation:
Mathematical Sciences Group, Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 5E6

Email:
browne@snoopy.usask.ca

**Bruce A. Watson**

Affiliation:
Department of Mathematics, University of the Witwatersrand, Private Bag 3, P O WITS 2050, South Africa

Email:
watson-ba@e-math.ams.org

DOI:
https://doi.org/10.1090/S0002-9947-02-03023-4

Keywords:
Eigenvalue asymptotics,
indefinite weight,
turning point

Received by editor(s):
January 12, 2002

Published electronically:
May 22, 2002

Article copyright:
© Copyright 2002
American Mathematical Society