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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!

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    Please look at this MathJax tutorial: http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference I've edited your problem this time. – 2017-02-04
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    I don't think the solutions you have are correct. Could you should how you got $u(r)$? – 2017-02-10

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