On the Existence of Eigenvalues of the Three-Particle Discrete Schrödinger Operator

We consider the three-particle Schrödinger operator , , associated with a system of three particles (of which two are bosons with mass and one is arbitrary with mass ) coupled by pairwise contact potentials and on the three-dimensional lattice . We prove that there exist critical mass ratio values and such that for sufficiently large and fixed the operator , , has at least one eigenvalue lying to the left of the essential spectrum for , at least two such eigenvalues for , and at least four such eigenvalues for .