Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Oscillation theory for indefinite Sturm-Liouville problems with eigenparameter-dependent boundary conditions

P. A. Bindinga1* and Patrick J. Brownea2*

a1 Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4

a2 Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 0W0

In previous papers we have studied oscillation properties of Sturm–Liouville problems (−Py′)′ + qy = λry, with λ-dependent boundary conditions, under various ‘definiteness’ conditions. Here we present a new, unified, approach which also covers cases previously untreated, e.g. of semidefinite weight, and also the fully indefinite problem.

(Received December 12 1995)

(Revised October 09 1996)


* Research of both authors is supported in part by grants from the NSERC of Canada. The first author was also supported by an I W. Killam Fellowship.