  We study the existence of non-trivial, non-negative periodic solutions for
systems of singular-degenerate parabolic equations with nonlocal terms and
satisfying Dirichlet boundary conditions. The method employed in this paper is
based on the Leray-Schauder topological degree theory. However, verifying the
conditions under which such a theory applies is more involved due to the
presence of the singularity. The system can be regarded as a possible model of
the interactions of two biological species sharing the same isolated territory,
and our results give conditions that ensure the coexistence of the two species.
