  We consider self-adjoint extensions of differential operators of the type $
(-\frac{d^2}{dr^2} + \frac{l(l+1)}{r^2})^3 $ on the real semi-axis for l=1,2
with two kinds of boundary conditions: first that nullify the value of a
function and its first derivative and second that nullify the 4th (l=1) or the
3rd (l=2) derivative. We calculate the expressions for the correponding
resolvents and derive spectral decompositions. These types of boundary
conditions are interesting from the physical point of view, especially the
second ones, which give an example of emergence of long-range action in
exchange for a singularity at the origin.
