Where can I find some information about: find the eigen values and eigen vectors $(\lambda,u)$ of the Sturm-Liouville problem
-$div(\rho^{\alpha+1}\nabla u)=\lambda\rho^\alpha u$
where $\alpha>-1$ and $\rho(x,y)=1-x^2-y^2$?
I'm working on $D=\{(x,y)\in\mathbb{R}^2:\;x^2+y^2\leq1\}$.
Thanks!