Sturm-Liouville form

English

Etymology

Named after Jacques Charles François Sturm (1803–1855) and Joseph Liouville (1809–1882).

Noun

Sturm-Liouville form (plural Sturm-Liouville forms)

1. (mathematics) the form of a real differential equation expressed as:

$${\frac {d}{dx}}\!\!\left[\,p(x){\frac {dy}{dx}}\right]+q(x)y=-\lambda \,w(x)y,$$

for given coefficient functions p(x), q(x), and w(x), an unknown function y = y(x) of the free variable x, and an unknown constant λ.