2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101994A model operator $H$ associated to a system of three-particles on the three dimensional lattice $\Z^3$ and interacting via pair non-local potentials is studied. The following results are proven: (i) the operator $H$ has infinitely many eigenvalues lying below the bottom of the essential spectrum and accumulating at this point, in the case, where both Friedrichs model operators $h_{μ_α}(0),α=1,2,$ have threshold resonances. (ii) the operator $H$ has a finite number of eigenvalues lying outside of the essential spectrum, in the case, where at least one of $h_{μ_α}(0), α=1,2,$ has a threshold eigenvalue.14 pagesMathematical PhysicsSpectral TheoryPrimary: 81Q10, Secondary: 35P20, 47N50text