I need to solve $\Delta ^{2} u = c $ inside a plane disk of radius a, using the Green's function expansion. The border condition is $u(a,\theta) = 0$. So I follow the standard procedure of finding the eigenfunctions for the homogeous equation $\Delta ^{2} u = c $.
And I get:
$u_{n} = r ^ {\lambda_{n}} (A_{n}\cos(\lambda_{n}\theta)+B_{n}\sin(\lambda_{n}\theta))$
But I can't apply the boundary condition, since it is independent from $\theta$.