Distribution of eigenvalues of a two-parameter system of differential equations

Author:
M. Faierman

Journal:
Trans. Amer. Math. Soc. **247** (1979), 45-86

MSC:
Primary 34B25; Secondary 34E05

MathSciNet review:
517686

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Abstract: In this paper two simultaneous Sturm-Liouville systems are considered, the first defined for the interval , the second for the interval , and each containing the parameters and . Denoting the eigenvalues and eigenfunctions of the simultaneous systems by and , respectively, , asymptotic methods are employed to derive asymptotic formulae for these expressions, as when is restricted to lie in a certain sector of the -plane. These results constitute a further stage in the development of the theory related to the behaviour of the eigenvalues and eigenfunctions of multiparameter Sturm-Liouville systems and answer an open question concerning the uniform boundedness of the .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0517686-7

Keywords:
Two-parameter systems,
simultaneous Sturm-Liouville systems,
eigenvalues,
eigenfunctions,
asymptotic formulae,
transition point,
Bessel functions

Article copyright:
© Copyright 1979
American Mathematical Society