Asymptotic behavior of solutions of a periodic reaction–diffusion system of a three-species of competition model

This paper concerns a three species periodic competition system which subjects to homogeneous Neumann boundary conditions. Using a result obtained by Ahmad and Lazer, we give some estimates and nonexistence results for the positive solutions of the system. Furthermore, we investigate the asymptotic behavior of the solutions of the system, definitely, we refer to that one species dies out and the other two coexist as time t tends to infinity.