Abstract:

Under homogeneous Dirichlet boundary conditions, a predator-prey model with predator cannibalism is considered. The existence and uniqueness of positive solutions are presented. By maximum principles and lower-upper solution methods, a prior estimate of positive solutions is firstly obtained. Then by Leray-Schauder theory and resorting to calculate fixed point indices of compact maps in cones, sufficient conditions for coexistence are given. Moreover, the uniqueness of positive solutions is derived under some conditions.

Key words: predator cannibalism; predatorprey; uniqueness