Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-12-01T04:08:44.672Z Has data issue: false hasContentIssue false

Asymptotic estimates for eigenvalues of right definite two parameter Sturm–Liouville problems

Published online by Cambridge University Press:  20 January 2009

Patrick J. Browne
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary Alberta, Canada, T2N 1N4
B. D. Sleeman
Affiliation:
Department of Mathematics and Computer Science, University of Dundee, Dundee DD1 4HN, Scotland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Precise asymptotic estimates for the eigenvalues of a uniformly right definite two parameter system of Sturm–Liouville problems are developed. The work extends recent results of B. P. Rynne.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

REFERENCES

1.Binding, P. A. and Browne, P. J., Positivity results for determinantal operators, Proc. Roy. Soc. Edinburgh 81A (1978), 267271.CrossRefGoogle Scholar
2.Binding, P. A. and Browne, P. J., Comparison cones for multiparameter eigenvalue problems, J. Math. Anal. Appl. 77 (1980), 132149.CrossRefGoogle Scholar
3.Faierman, M., On the distribution of the eigenvalues of a two-parameter system of ordinary differential equations of the second order, SIAM J. Math. Anal. 8 (1977), 854870.CrossRefGoogle Scholar
4.Faierman, M., Distribution of eigenvalues of a two-parameter system of differential equations, Trans. Amer. Math. Soc. 247 (1979), 4586.CrossRefGoogle Scholar
5.Poschel, J. and Trubowitz, E., Inverse Spectral Theory (Academic Press, London, 1987).Google Scholar
6.Rynne, B. P., The asymptotic distribution of the eigenvalues of right definite multiparameter Sturm-Liouville systems, Proc. Edinburgh Math. Soc., to appear.Google Scholar