Non-constant positive steady-states of a diffusive predator–prey system in homogeneous environment

In this paper, we investigate the existence and non-existence of non-constant positive steady-states of a diffusive predator–prey interaction system under homogeneous Neumann boundary condition. In homogeneous environment, we show that the predator–prey model with Leslie–Gower functional response has no non-constant positive solution, but the system with a general functional response may have at least one non-constant positive steady-state under some conditions.