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

Non-trivial, non-negative periodic solutions of a system of singular-degenerate parabolic equations with nonlocal terms