Monotonicity of the eigenvalues of the two-particle Schrodinger operatoron a lattice

We consider the two-particle Schrodinger operator H (k), (k is an element of T-3 (-pi, pi](3) is the total quasimomentum of a system of two particles) corresponding to the Hamiltonian of the two-particle system on the three-dimensional lattice Z(3). It is proved that the number N (k) N (k((1)), k((2)), k((3))) of eigenvalues below the essential spectrum of the operator H (k) is nondecreasing function in each k((i)) is an element of [0, pi], i = 1, 2, 3. Under some additional conditions potential (v) over cap, the monotonicity of each eigenvalue z(n) (k) z(n)(k((1)), k((2)), k((3))) of the operator H (k) in k((i)) is an element of [0, pi] with other coordinates k being fixed is proved.