Invariant Subspaces and Eigenvalues of the Three-Particle Discrete Schrödinger Operators

We consider three-particle Schr & ouml;dinger operator H-mu,H-gamma(K), K is an element of T-3, associated to a system of three particles (two of them are bosons with mass 1 and one is an arbitrary with mass m = 1/ gamma < 1), interacting via zero-range pairwise potentials mu > 0 and lambda > 0 on the three dimensional lattice Z(3). It is proved that there exist critical value of ratio of mass gamma = gamma(1) and gamma = gamma(2) such that the operator H-mu,H-gamma(0) 0 = (0, 0, 0), has a unique eigenvalue for gamma is an element of (0, gamma(1)), has two eigenvalues for gamma is an element of (gamma(1),gamma(2)) and four eigenvalues for gamma is an element of (gamma(2), +infinity), located on the left-hand side of the essential spectrum for large enough mu > 0 and fixed lambda > 0.