We study a generalized Hubbard model in the $U=\ensuremath{\infty}$ limit with use of the slave-boson technique. The $N=\ensuremath{\infty}$ theory describes a Fermi liquid with a strongly renormalized effective mass. The
N1 corrections give rise to different superconducting instabilities depending on the band structure and the filling factor. For low densities there is a
p-wave instability while close to half filling in the cubic lattice we find a
d-wave instability. We also calculate Fermi-liquid parameters.
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.
Considering Hubbard models with infinite U , N degrees of freedom per site, and hopping terms between nearest and second-nearest neighbours on a square lattice, and using a formulation with X -operators, the leading contributions at large N to the anomalous self-energy and the linearized Eliashberg equation are calculated. Some of these terms have the form of Fock-like terms with an effective two-particle interaction, others have a different structure and have not been discussed previously. Calculating transition temperatures, we find that the new terms found in our 1/ N expansion compensate the other terms nearly perfectly suppressing superconducting instabilities to extremely small temperatures.