I've been stuck on finding the eigenfunctions/values for the radial part of the Sturm Liouville laplace operator in spherical coordinates for two given boundry conditions $u(r1)=u(r2)=0$.
I have the equation $-\Delta u(r)=\lambda u(r)$.
I've found that for $\lambda > 0$ that $u(r) = A\cos(\sqrt{\lambda}r) + B\sin(\sqrt{\lambda}r)$.
Using that $A$ and $B$ should be positive and after plugging in the boundry conditions I conclude that $\cot(\sqrt{\lambda}r_1)=\cot(\sqrt{\lambda}r_2)$.
Am I on the right track? If so, what can I say about $\lambda$?
Thankfull for any help/hints!