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On a Perturbation in a Two-Parameter Ordinary Differential Equation of the Second Order

Published online by Cambridge University Press:  20 November 2018

M. Faierman
M. Faierman*
Affiliation:
Loyola College, Montreal, Quebec
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Let us consider the linear system in the two parameters λ and μ; i. e.,

1.1

1.2

and where for the moment we shall assume both b(x) and q(x) are real-valued, continuous functions in [0, 1].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 25 - 33
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Faierman, M., Ph.D. Thesis, Univ. of Toronto, Toronto, 1966.Google Scholar
2. Meixner, J. and Schäfke, F. W., Mathieusche Funktionen und Sphäroidfunktionen, Springer-Verlag, Berlin, 1954.Google Scholar
3. Faierman, M., Asymptotic formulae for the eigenvalues of a two-parameter ordinary differential equation, Trans. Amer. Math. Soc, (to appear).Google Scholar
4. Coddington, E. A. and Levinson, N., Theory of ordinary differential equations, McGraw- Hill, New York, 1955.Google Scholar
5. Whittaker, E. T., and Watson, G. N., A course of modern analysis, Cambridge Univ. Press, New York, 1965.Google Scholar
6. Titchmarsh, E. C., Eigenfunction expansions, Part II. Oxford Univ., New York, 1958.Google Scholar