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.