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Sturm–Liouville problems with eigenparameter dependent boundary conditions

Published online by Cambridge University Press:  20 January 2009

P. A. Binding ,
P. J. Browne  and
K. Seddighi
P. A. Binding
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada
P. J. Browne
Affiliation:
Department of Mathematics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 0W0, Canada
K. Seddighi
Affiliation:
Department of Mathematics, University of Shiraz, Iran71454
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Abstract

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Sturm theory is extended to the equation

for 1/p, q, r∈L1 [0, 1] with p, r > 0, subject to boundary conditions

and

Oscillation and comparison results are given, and asymptotic estimates are developed. Interlacing of eigenvalues with those of a standard Sturm–Liouville problem where the boundary conditions are ajy(j) = cj(py′)(j), j=0, 1, forms a key tool.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 1 , February 1994 , pp. 57 - 72
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

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