  The feasibility of a perturbation expansion for Green's functions of the t-J
model directly in terms of X-operators is demonstrated using the Baym- Kadanoff
functional method. As an application we derive explicit expressions for the
kernel of the linearized equation for the superconducting order parameter in
leading order of a 1/N expansion. The linearized equation is solved numerically
on a square lattice. We find that a reasonably strong instability occurs only
for even frequency pairing with d-wavelike symmetry. Results for the transition
temperature and the effective interaction are given as a function of doping.
