Uniqueness of Coexistence State of General Competition Model for Several Competing Species

Abstract

We study the uniqueness of the positive solution for the generalized Lotka-Volterra competition model for several competing species. Some uniqueness results when self-reproduction, self-limitation, and competition rates are positive constants have been obtained over the last decade. We generalize these results when self-limitation and competition are mere general functions. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equatins.