Finiteness of the discrete spectrum of the three-particle Schrodinger equation on a lattice

Consideration is given to the Hamiltonian of a system of three identical quantum particles on a lattice that interact via pairwise contact attractive potentials. Finiteness of the three-particle bound states is proved for the three-dimensional discrete Schrodinger operator on the condition that the operators describing the two-particle subsystems have no virtual levels. For high dimensions (upsilon greater than or equal to 5), the finiteness of three-particle bound states is also proved in the presence of virtual levels.