Existence of the eigenvalues of a tensor sum of the Friedrichs models with rank 2 perturbation

In the paper we consider a tensor sum $H_{\mu,\lambda}$, $\mu,\lambda>0$ of two Friedrichs models $h_{\mu,\lambda}$ with rank two perturbation. The Hamiltonian $H_{\mu,\lambda}$ is associated with a system of three quantum particles on one-dimensional lattice. We investigate the number and location of the eigenvalues of $H_{\mu,\lambda}$. The existence of eigenvalues located respectively inside, in the gap, and below the bottom of the essential spectrum of $H_{\mu,\lambda}$ is proved.