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STURM–LIOUVILLE PROBLEMS WITH BOUNDARY CONDITIONS RATIONALLY DEPENDENT ON THE EIGENPARAMETER. I

Published online by Cambridge University Press:  14 October 2002

Paul A. Binding ,
Patrick J. Browne  and
Bruce A. Watson
Paul A. Binding
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4 (binding@ucalgary.ca)
Patrick J. Browne
Affiliation:
Mathematical Sciences Group, Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada, S7N 5E6 (browne@admin.usask.ca)
Bruce A. Watson
Affiliation:
Department of Mathematics, University of the Witwatersrand, Private Bag 3, PO WITS 2050, South Africa (watson@maths.wits.ac.za)
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Abstract

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We consider the Sturm–Liouville equation

$$ -y''+qy=\lambda y\quad\text{on }[0,1], $$

subject to the boundary conditions

$$ y(0)\cos\alpha=y'(0)\sin\alpha,\quad\alpha\in[0,\pi), $$

and

$$\frac{y'}{y}(1)=a\lambda+b-\sum_{k=1}^N\frac{b_k}{\lambda-c_k}. $$

Topics treated include existence and asymptotics of eigenvalues, oscillation of eigenfunctions, and transformations between such problems.

AMS 2000 Mathematics subject classification: Primary 34B24; 34L20

Keywords

Sturm–Liouvilleeigenparameter-dependent boundary conditioneigenfunction oscillationeigenvalue asymptotics
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 3 , October 2002 , pp. 631 - 645
Copyright
Copyright © Edinburgh Mathematical Society 2002