  It is shown that the one-dimensional nonlinear Schr\"odinger equation with a
dissipative periodic potential, nonlinear losses and linear pump allow for the
existence of stable nonlinear Bloch states which are attractors. The model
describes a Bose-Einstein condensate with inelastic two- and three-body
interactions loaded in an optical lattice with losses due to inelastic
interactions of the atoms with photons.
