Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-30T21:58:16.040Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillation theory for indefinite 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
Get access Rights & Permissions [Opens in a new window]

Extract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 6 , 1997 , pp. 1123 - 1136
Copyright
Copyright © Royal Society of Edinburgh 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Binding, P. A. and Browne, P. J.. Application of two-parameter spectral theory to symmetric generalized eigenvalue problems. Appl. Anal. 29 (1988), 107–42.CrossRefGoogle Scholar
2Binding, P. A. and Browne, P. J.. Spectral properties of two parameter eigenvalue problems II. Proc. Roy. Soc. Edinburgh Sect. A 106 (1987), 39–53 (Corrigendum with R. H. Picard, ibid. 115 (1990), 87–90).Google Scholar
3Binding, P. A. and Browne, P. J.. Application of two parameter eigencurves to Sturm–Liouville problems with eigenparameter-dependent boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995), 1205–18.CrossRefGoogle Scholar
4Binding, P. A. and Browne, P. J.. Left definite Sturm–Liouville problems with eigenparameterdependent boundary conditions (submitted).Google Scholar
5Binding, P. A., Browne, P. J. and Seddighi, K.. Sturm–Liouville problems with eigenparameterdependent boundary conditions. Proc. Edinburgh Math. Soc. 37 (1993), 57–72.CrossRefGoogle Scholar
6Binding, P. A. and Seddighi, K.. On root vectors of self-adjoint pencils. J. Fund. Anal. 70 (1987), 117–25.Google Scholar
7Dijksma, A. and Langer, H.. Operator theory and ordinary differential operators (Fields Institute Lectures, October, 1994).Google Scholar
8Everitt, W. N., Kwong, N. K. and Zetti, A.. Oscillation of eigenfunctions of weighted regular Sturm–Liouville problems. J. London Math. Soc. 27 (1983), 106–20.CrossRefGoogle Scholar
9Fulton, C. T.. Two point boundary value problems with eigenvalue parameter contained in the boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 293–308.CrossRefGoogle Scholar
10Langer, H.. Spectral functions of definitizable operators in Krein spaces. Lecture Notes in Math. 948 (1982), 1–46.Google Scholar
11Langer, H. and Schneider, A.. On spectral properties of regular quasidefinite pencils F — λG. Results in Math. 19 (1991), 89–109.CrossRefGoogle Scholar
12Reid, W. T.. Sturmian Theory for Ordinary Differential Equations (Berlin: Springer, 1980).Google Scholar
13Walter, J.. Regular eigenvalue problems with eigenvalue parameter in the boundary conditions. Math. Z. 133 (1973), 301–12.CrossRefGoogle Scholar