The existence and location of eigenvalues of the one particle discrete\n Schroedinger operators

We consider a quantum particle moving in the one dimensional lattice Z and\ninteracting with a indefinite sign external field v. We prove that the\nassociated discrete Schroedinger operator H can have one or two eigenvalues,\nsituated as below the bottom of the essential spectrum, as well as above its\ntop. Moreover, we show that the operator H can have two eigenvalues outside of\nthe essential spectrum such that one of them is situated below the bottom of\nthe essential spectrum, and other one above its top.\n