On small perturbations of the Schrodinger operator with a periodic potential

Consideration is given to small perturbations of a potential, periodic with respect to the variables x(j), j = 1, 2, 3, by a function periodic in x(1) and x(2) that decays exponentially as \x(3)\ --> infinity. It is shown that in the neighborhood of energies corresponding to the extrema in the third quasimomentum component of nondegenerate eigenvalues of the Schrodinger operator, with the periodic potential considered in a cell, there exists a unique solution (up to within a numerical factor) to the integral equation describing both the eigenvalues and resonance levels. The asymptotic behavior of the eigenvalues and resonance levels is investigated.