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Regular and singular Sturm–Liouville problems with coupled boundary conditions

Published online by Cambridge University Press:  14 November 2011

P. B. Bailey ,
W. N. Everitt  and
A. Zettl
P. B. Bailey
Affiliation:
1008 Oro-Real N.E., Albuquerque, NM 87123, U.S.A.
W. N. Everitt
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Edgebaston, Birmingham B15 2TT, U.K.
A. Zettl
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115-2880, U.S.A.
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Extract

Eigenvalues of both regular and singular Sturm–Liouville (S–L) problems with general coupled self-adjoint boundary conditions are characterised. This characterisation, although elementary, appears to be new even in the regular case. The singular characterisation is an exact parallel of the regular one and reduces to it. One application yields inequalities among the eigenvalues of different coupled boundary conditions. This is a far-reaching extension, even in the regular case, of the well-known relationship among the periodic and semiperiodic eigenvalues.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 3 , 1996 , pp. 505 - 514
Copyright
Copyright © Royal Society of Edinburgh 1996

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