The Distribution of the Eigenvalues

Abstract

It follows from the results of Chapter 3 that if the function q(x) of the Sturm-Liouville operator

$$ {L_y} = - y'' + q(x)y,\,a < x < , $$

(1.1)

is bounded from below, and tends to +∞ as x → a or x → b (or both), then the spectrum of L is discrete (assuming that at least one of the endpoints is singular; furthermore, if at least one of them is regular, a boundary condition should be specified on it).