Conditions for the existence of eigenvalues of a three-particle lattice model Hamiltonian

In this article, we present a three-particle lattice model Hamiltonain $H_{\mu,\lambda}$, $\mu,\lambda>0$ by making use of non-local potential. The Hamiltonian under consideration acts as a tensor sum of two Friedrichs models $h_{\mu,\lambda}$ which comprises a rank $2$ perturbation associated with a system of three quantum particles on a ${d}$-dimensional lattice. The current study investigates the number of eigenvalues associated with the Hamiltonian. Furthermore, we provide the suitable conditions on the existence of eigenvalues localized inside, in the gap and below the bottom of the essential spectrum of $H_{\mu,\lambda}$.