Talk:Sturm–Picone comparison theorem

Isnt this commonly known as the oscillation theorem?

Also, there are many other versions. For example, a very useful result is this: Consider the eigenvalue problem $$y''+p(x)y = \lambda y $$ with dirichlet boundary conditions on some bounded interval and with p(x)>0. Then the eigenvalues form an infinite a decreasing sequence $$\lambda_0 > \lambda_1 > \lambda_2 ...$$ The eigenfunction $$y_i$$ corresponding to the eigenvalue $$\lambda_i$$ has precisely i roots.

There are other versions, which involve the ratios v'/v etc...

Can somebody who is more familiar than me with this, add these versions to the page? Also is it ok to redirect "oscillation theorem" and "sturm theorem", "sturm lemma", "sturm oscillation theorem" to this page? Personally i've heard of "sturm theorem" but not of "sturm-picone"... which name is more common?

Asympt (talk) 04:35, 24 March 2009 (UTC)