Essential and discrete spectrum of the three-particle Schroedinger operator on lattice

The system of three quantum particles (two of them are bosons and the third one is an arbitrary particle), interacting through the attraction pairing contact potentials, is considered on the three-dimensional lattice. The essential spectrum is described; the existence of the Efimov effect is proved for the cases, when two or three two-particle subsystems of the three-particle system maintain the virtual levels on the left edge of the three-particle essential spectrum by the zero value of the total quasi-momentum. The finiteness of the bound states number at low values of the total quasi-momentum is indicated