Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-12-01T00:21:08.323Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Eastham, M. S. P. The Spectral Theory of Periodic Differential Equations (Edinburgh: Scottish Academic Press, 1973).Google Scholar
2Krall, A. M. and Zettl, A.. Singular self-adjoint Sturm–Liouville problems. Differential Integral Equations 1 (1988), 423–32.CrossRefGoogle Scholar
3Möller, M.. On the unboundedness below of the Sturm–Liouville operator (Preprint).Google Scholar
4Naimark, M. A.. Linear Differential Operators: II (New York: Ungar, 1968).Google Scholar
5Niessen, H.-D. and Zettl, A.. Singular Sturm–Liouville problems: The Freidrichs extension and comparison of eigenvalues. Proc. London Math. Soc. (3) 64 (1992), 545–78.Google Scholar
6Weidmann, J.. Linear Operators in Hilbert Spaces, Graduate Texts in Mathematics 68 (Berlin: Springer, 1980).CrossRefGoogle Scholar
7Weidman, J.. Spectral Theory of Ordinary Differential Operators, Lecture Notes in Mathematics 1258 (Berlin: Springer: 1987).CrossRefGoogle Scholar