  It is shown that solutions to the 2nd order BFKL eigenvalue equation exist
for arbitrary large real values of the complex angular momentum $j$. This
corresponds to a cut in the complex $j$ plane along the whole real axis, and it
makes the use of the complex angular momentum variable for the calculation of
the high-energy behavior somewhat questionable. The eigenfunctions contain
non-perturbative pieces which behave as $\exp(-1/\alpha_s b)$ and have no
counterpart in the leading-log BFKL equation. The high-energy behavior of the
2nd order BFKL Green function as found by other authors, is reproduced by
excluding these non-perturbative pieces of the eigenfunctions.
