Essential and discrete spectra of the three-particle Schrodinger operator on a lattice

We consider the system of three quantum particles (two are bosons and the third is arbitrary) interacting by attractive pair contact potentials on a three-dimensional lattice. The essential spectrum is described. The existence of Hie Efimov effect is proved in the case where either two or three two-particle subsystems of the three-particle system have virtual levels at the left edge of the three-particle essential spectrum for zero total quasimomentum (K = 0). We also show that for small values of the total quasimomentum (K not equal 0), the number of bound states is finite.