Existence of an isolated band in a system of three particles in an optical lattice

We prove the existence of two- and three-particle bound states of the Schrodinger operators h(mu)(k), k is an element of T-d and H-mu(K), K is an element of T-d associated to Hamiltonians h(mu) and H-mu of a system of two and three identical bosons on the lattice Z(d), d = 1, 2 interacting via pairwise zero-range attractive mu < 0 or repulsive mu > 0 potentials. As a consequence, we show the existence of an isolated band in the two- and three-bosonic systems in an optical lattice.