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STURM–LIOUVILLE PROBLEMS WITH REDUCIBLE BOUNDARY CONDITIONS

Published online by Cambridge University Press:  25 January 2007

Paul A. Binding ,
Patrick J. Browne  and
Bruce A. Watson
Paul A. Binding
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada ([email protected])
Patrick J. Browne
Affiliation:
Mathematical Sciences Group, Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E6, Canada ([email protected])
Bruce A. Watson
Affiliation:
School of Mathematics, University of the Witwatersrand, Private Bag 3, PO WITS 2050, South Africa ([email protected])
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Abstract

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The regular Sturm–Liouville problem

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

is studied subject to boundary conditions

$$ P_j(\lambda)y'(j)=Q_j(\lambda)y(j),\quad j=0,1, $$

where $q\in L^1(0,1)$ and $P_j$ and $Q_j$ are polynomials with real coefficients. A comparison is made between this problem and the corresponding ‘reduced’ one where all common factors are removed from the boundary conditions. Topics treated include Jordan chain structure, eigenvalue asymptotics and eigenfunction oscillation.

Keywords

Primary 34B2546D0547E05Sturm–Liouville problemeigenparameter-dependent boundary conditionsJordan chain
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 3 , October 2006 , pp. 593 - 608
Copyright
Copyright © Edinburgh Mathematical Society 2006