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.
