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The asymptotic distribution of the eigenvalues of multiparameter Sturm–Liouville systems II

Published online by Cambridge University Press:  20 January 2009

Bryan P. Rynne
Affiliation:
Department of MathematicsHeriot-Watt UniversityRiccartonEdinburgh EH14 4AS
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Abstract

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In a previous paper we studied the asymptotic distribution of the multiparameter eigenvalues of uniformly right definite multiparameter Sturm–Liouville eigenvalue problems. In this paper we extend the analysis to deal with multiparameter Sturm–Liouville problems satisfying uniform left definiteness, and non-uniform left and right definiteness.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

REFERENCES

1.Atkinson, F. V., Discrete and Continuous Boundary Value Problems (Academic Press, New York, 1961).Google Scholar
2.Binding, P., Multiparameter definiteness conditions, Proc. Roy. Soc. Edinburgh 89A (1981), 319332.CrossRefGoogle Scholar
3.Binding, P., Dual variational approaches to multiparameter eigenvalue problems, J. Math. Anal. Appl. 92 (1983), 96113.CrossRefGoogle Scholar
4.Binding, P., Nonuniform right definiteness, J. Math. Anal. Appl. 102 (1984), 233243.CrossRefGoogle Scholar
5.Binding, P. and Volkmer, H., Existence and uniqueness of indexed multiparametric eigenvalues. J. Math. Anal. Appl 116 (1986), 131146.CrossRefGoogle Scholar
6.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), 391397.CrossRefGoogle Scholar
7.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
8.Faierman, M., Distribution of eigenvalues of a two-parameter system of differential equations. Trans. Amer. Math. Soc 247 (1979), 4586.CrossRefGoogle Scholar
9.Ince, E., Ordinary Differential Equations (Dover reprint, New York, 1956).Google Scholar
10.Rynne, B. P., The asymptotic distribution of the eigenvalues of right definite multi-parameter Sturm—Liouville systems, Proc. Edinburgh Math. Soc. 36 (1993), 3547.CrossRefGoogle Scholar
11.Sleeman, B. D., Klein oscillation theorems for multiparameter eigenvalue problems in ordinary differential equations, Nieuw Arch. Wisk. 27 (1979), 341362.Google Scholar
12.Kingman, J. F. C. and Taylor, S. J., Introduction to Measure and Probability (Cambridge University Press, 1966).CrossRefGoogle Scholar