Sturm-Liouville Theory

Abstract

1. In a series of articles dating from 1836–1837, Sturm and Liouville created a whole new subject in mathematical analysis. The theory, later known as Sturm-Liouville theory, deals with the general linear second-order differential equation

$$(k(x)V'(x))' + (g(x)r - l(x))V(x) = 0\quad for\;x \in (\alpha ,\beta ),$$

(1)

with the imposed boundary conditions

$$k(x)V'(x) - hV(x) = 0\quad for\;x = \alpha ,$$

(2)

$$k(x)V'(x) + HV(x) = 0\quad for\;x = \beta .$$

(3)