Sturm-Liouville problem on unit disk

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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!