The Number of Eigenvalues of the Three-Particle Schrodinger Operator on Three Dimensional Lattice

We consider the three-particle discrete Schrodinger operator H-mu,H-gamma(K), K is an element of T-3 associated to a system of three particles (two fermions and one another particle) interacting through zero range pairwise potential mu > 0 on the three-dimensional lattice Z(3). It is proved that there exist positive numbers gamma(2) > gamma(1) that the operator H-mu,H-gamma(pi), pi = (pi, pi, pi) for gamma is an element of(0, gamma(1)) has no eigenvalue, for gamma is an element of(gamma(1,)gamma(2)) has a simple eigenvalue and for gamma > gamma(2) it has three eigenvalues lying below the essential spectrum for sufficiently large mu.