The Uniqueness of Positive Solutions for a Predator-Prey Model with B-D Functional Response

摘要

In this paper, we investigate a diffusive predator-prey model with Beddington-DeAngelis functional response, which is subject to homogeneous Dirichlet boundary conditions. Based on the fixed point index theory, a good understanding of the existence, uniqueness and stability of positive solutions is obtained when is sufficiently small. We always reduce the proof of uniqueness and stability to the proof of the fact that any possible positive solution is non-degenerate and linearly stable.