ABSTRACT
In this chapter, our concern is to extend to the multiparameter case the following statements concerning the Sturm-Liouville problem (8.1.1)–(8.1.2):
(i) if p(x) is positive in (a, b), the n-th eigenvalue in ascending order is of magnitude n2, and the eigenvalues accumulate only at +∞,
(ii) if p(x) changes sign, but a certain quadratic form∫ b a
y{y′′ − q(x)y − µp(x)y} dx (8.1.3)
is negative-definite, there is both an ascending and descending sequence of eigenvalues, the n-th in each case being of order n2, eigenvalues accumulating both at +∞ and at −∞.
