  In analogy with ordinary BCS superconductivity, we identify possible pairing
instabilities with poles in a certain class of Green functions of the
two-dimensional repulsive Hubbard model, which normally signify bound states.
Relating the gap to the location of these poles, we find that these
instabilities exist in the range of hole doping between 0.03 and 0.24. The
magnitude of the gap can be calculated without introducing an explicit cut-off,
and for reasonably large coupling U/t = 10, the maximum gap is on the order of
0.08 in units of the hopping parameter t.
