Coexistence periodic solutions of a doubly nonlinear parabolic system with Neumann boundary conditions

This paper is concerned with a competitive and cooperative mathematical model for two biological populations which dislike crowding, diffuse slowly and live in a common territory under different kind of intra- and inter-specific interferences. The model consists of a system of two doubly nonlinear parabolic equations with nonlocal terms and Neumann boundary conditions. Based on the theory of the Leray–Schauder degree, we obtain the coexistence periodic solutions, namely the existence of two non-trivial non-negative periodic solutions representing the densities of the two interacting populations, under different intra- and inter-specific interferences on their natural growth rates.