Coexistence, Stability, and Limiting Behavior in a One-Predator-Two-Prey Model

This paper considers a reaction-diffusion system that models the situation in which a predator feeds on two prey species. The existence of a positive steady-state solution as well as the existence and stability of various semitrivial steady-state solutions is obtained in terms of the natural growth rates of the three species. The present paper also gives some explicit information on the limiting behavior of the time-dependent solution to these steady states.