On levels of a weakly perturbed periodic Schrodinger operator

We consider the Schrodinger operator with a periodic potential perturbed by a function which is periodic in two variables and exponentially decreases in third variable. When the perturbation is small it is proved that the levels (eigenvalues or resonances) exist near the stationary points of the eigenvalues of the periodic Schrodinger operator in the cell with respect to the third component of quasimomentum. The behaviour of these levels is investigated.