  We consider fermions on a 2D lattice interacting repulsively on the same site
and attractively on the nearest neighbor sites. The model is relevant, for
instance, to study the competition between antiferromagnetism and
superconductivity in a Kondo lattice. We first solve the two-body problem to
show that in the dilute and strong coupling limit the s-wave Bose condensed
state is always the ground state. We then consider the many-body problem and
treat it at mean-field level by solving exactly the usual gap equation. This
guarantees that the superconducting wave-function correctly vanishes when the
two fermions (with antiparallel spin) sit on the same site. This fact has
important consequences on the superconducting state that are somewhat unusual.
In particular this implies a radial node-line for the gap function. When a next
neighbor hopping t' is present we find that the s-wave state may develop nodes
on the Fermi surface.
