Existence of non-constant positive stationary solutions of the shadow predator-prey systems with Allee effect - Bao, Zhenhua; Liu, He (Advances in difference equations, 2014)
In this paper, we consider the dynamics of the shadow system of a kind of homogeneous diffusive predator-prey system with a strong Allee effect in prey. We mainly use the time-mapping methods to prove the existence and non-existence of the non-constant positive stationary solutions of the system in the one dimensional spatial domain. The problem is assumed to be subject to homogeneous Neumann boundary conditions. MSC: 35K57, 35B09.