  It is shown that the mean-field description of a boson-fermion mixture with a
dominating fermionic component, loaded in a one-dimensional optical lattice, is
reduced to the nonlinear Schr\"{o}dinger equation with a periodic potential and
periodic nonlinearity. In such system there exist localized modes having
peculiar properties. In particular, for some regions of parameters there exists
a lower bound for a number of atoms necessary for creation of a mode, while for
other domains small amplitude gap solitons are not available in vicinity of
either of the gap edges. We found that the lowest branch of the symmetric
solution may either exist only for a restricted range of energies in a gap or
does not exist, unlike in pure bosonic condensates. The simplest bifurcations
of the modes are shown and stability of the modes is verified numerically.
