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Asymptotic spectrum of multiparameter eigenvalue problems

Published online by Cambridge University Press:  20 January 2009

Hans Volkmer
Hans Volkmer
Affiliation:
Department of Mathematical SciencesUniversity Of Wisconsin-MilwaukeeP. O. Box 413Milwaukee, WI 53201, USA
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Abstract

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Results are given for the asymptotic spectrum of a multiparameter eigenvalue problem in Hilbert space. They are based on estimates for eigenvalues derived from the minim un-maximum principle. As an application, a multiparameter Sturm-Liouville problem is considered.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 1 , February 1996 , pp. 119 - 132
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Atkinson, F. V., Multiparameter Eigenvalue Problems (Academic Press, New York, 1972).Google Scholar
2. Atkinson, F. V., On the essential spectrum in the non-singular Sturm-Liouville multipara-meter case, Lecture at 3rd International Workshop on Multiparameter Theory, Calgary, 1985.Google Scholar
3. Atkinson, F. V. and Mingarelli, A. B., Asymptotics of the number of zeros and of the eigenvalues of general weighted Sturm-Liouville problems, J. Reine Angew. Math. 375 (1987), 380–393.Google Scholar
4. Binding, P. A. and Browne, P. J., A variational approach to multiparameter eigenvalue problems in Hilbert space, SIAM J. Math. Anal. 9 (1978), 1054–1067.CrossRefGoogle Scholar
5. Binding, P. A. and Browne, P. J., Comparison cones for multiparameter eigenvalue problems, J. Math. Anal. Appl. 77 (1980), 132–149.CrossRefGoogle Scholar
6. Binding, P. A., Browne, P. J. and Seddighi, K., Two parameter asymptotic spectra, Resultate Math. 21 (1992), 12–23.CrossRefGoogle Scholar
7. Binding, P. A., Browne, P. J. and Seddighi, K., Two parameter asymptotic spectra in the uniformly elliptic case, preprint (1994).Google Scholar
8. Browne, P. J. and Sleeman, B. D., Asymptotic estimates for eigenvalues of right definite two parameter Sturm-Liouville problems, Proc. Edinburgh Math. Soc. 36 (1993), 391–397.CrossRefGoogle Scholar
9. Faierman, M., Distribution of eigenvalues of a two-parameter system of differential equations, Trans. Amer. Math. Soc. 247 (1979), 45–86.CrossRefGoogle Scholar
10. Rynne, B. P., The asymptotic distribution of the eigenvalues of right definite multiparameter Sturm-Liouville systems, Proc. Edinburgh Math. Soc. 36 (1992), 35–47.CrossRefGoogle Scholar
11. Turyn, L., Sturm-Liouville problems with several parameters, J. Differential Equations 38 (1980), 239–259.CrossRefGoogle Scholar
12. Volkmer, H., Multiparameter Eigenvalue Problems and Expansion Theorems (Lecture Notes in Math. 1356, Springer, Berlin-Heidelberg-New York, 1988).CrossRefGoogle Scholar
13. Weinstein, A. and Stenger, W., Methods of Intermediate Problems of Eigenvalues (Academic Press, New York, 1972).Google Scholar