Coexistence states of a periodic cooperative reaction-diffusion system with nonlinear functional response

In this paper, by using the existence and comparison conclusions for the T-periodic quasi-monotone nondecreasing system, we investigate a cooperative system with fractional functional response and the homogeneous Dirichlet boundary conditions. We mainly discuss the existence, uniqueness and nonexistence problems of positive solutions of the system by the method of upper and lower solutions. The numerical examples show that the relevant results hold with certain parameter values.