LAUSR

This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation. We obtain a critical value λ 1 D (Ω 0 ), and demonstrate that the existence of the predator in $${\overline \Omega _0}$$ Ω ¯ 0 only depends on the relationship of the growth rate μ of the predator and λ 1 D (Ω 0 ), not on the prey. Furthermore, when μ < λ 1 D (Ω 0 ), we obtain the existence and uniqueness of its positive steady state solution, while when μ ≥ λ 1 D (Ω 0 ), the predator and the prey cannot coexist in $${\overline \Omega _0}$$ Ω ¯ 0 . Our results show that the coexistence of the prey and the predator is sensitive to the size of the crowding region $${\overline \Omega _0}$$ Ω ¯ 0 , which is different from that of the classical Lotka-Volterra predator-prey model.