Vol. 90, No. 2, 1980

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Bounds for the eigenfunctions of a two-parameter system of ordinary differential equations of the second order

Melvin Faierman

Vol. 90 (1980), No. 2, 335–345

In previous papers the author has shown that, in contrast to the one-parameter case, the normalized eigenfunctions of two simultaneous Sturm-Liouville systems in two parameters are not necessarily uniformly bounded. Moreover, best possible bounds for the normalized eigenfunctions were also derived. However these results were only established under the assumption that the coefficients of our differential equations satisfied certain special conditions. Hence, in order to deal with problems which often arise in physical practice, it is important to extend our results to the case where the coefficients of our differential equations satisfy more general conditions then hitherto supposed. Accordingly, it is the object of this paper to derive best possible bounds for the normalized eigenfunctions of the simultaneous two-parameter systems in question under much weaker restrictions on their coefficients than was previously assumed.

Mathematical Subject Classification 2000
Primary: 34B25, 34B25
Secondary: 34C11
Received: 27 October 1976
Revised: 2 October 1979
Published: 1 October 1980
Melvin Faierman