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Application of two parameter eigencurves to Sturm–Liouville problems with eigenparameter-dependent boundary conditions

Published online by Cambridge University Press:  14 November 2011

P. A. Binding  and
Patrick J. Browne
P. A. Binding
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, CanadaT2N 1N4
Patrick J. Browne
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan, CanadaS7N 0W0
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Abstract

Oscillation, comparison and asymptotic theory for the Sturm-Liouville problem

with 1/p, q, r ε L1 ([0, 1]), p, r > 0, are studied subject to eigenvalue-dependent boundary conditions

This continues previous work on cases with (− 1)j δj ≦ 0 where δj = ajdj − bjcj. We now consider the remaining sign conditions for δj, exploiting the interplay between the graph of cot θ− (λ, 1), for a modified Prüfer angle θ−, and the eigencurves of a related two-parameter problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 6 , 1995 , pp. 1205 - 1218
Copyright
Copyright © Royal Society of Edinburgh 1995

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