On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice

On three-dimensional lattice we consider a system of three quantum particles (two of them are identical (fermions) and the third one is of another nature) that interact with the help of paired short-range potentials of attraction. We prove the finiteness of a number of bound states of respective Schrödinger operator in a case when potentials satisfy some conditions and the zero is a regular point for two-particle subhamiltonian. We find a set of particles masses' values such that the Schrödinger operator may have only finite number of eigenvalues lying to the left from essential spectrum.