Discrete spectrum of a noncompact perturbation of a three-particle Schrödinger operator on a lattice

We consider a system of three arbitrary quantum particles on a three-dimensional lattice interacting via attractive pair-contact potentials and attractive potentials of particles at the nearest-neighbor sites. We prove that the Hamiltonian of the corresponding three-particle system has infinitely many eigenvalues. We also list different types of attractive potentials whose eigenvalues can be to the left of the essential spectrum, in a gap in the essential spectrum, and in the essential spectrum of the considered operator.