The existence of bound states in a system of three particles in an optical lattice

We consider the hamiltonian H mu, mu is an element of R of a system of three-particles ( two identical fermions and one different particle) moving on the lattice Z(d), d = 1, 2 interacting through repulsive (mu > 0) or attractive (mu < 0) zero-range pairwise potential mu nu. We prove for any mu not equal 0 the existence of bound states of the discrete three-particle Schrodinger operator H-mu( K), K is an element of T-d being the three-particle quasi-momentum, associated to the hamiltonian H-mu.