The Existence and Uniqueness of a Positive Solution of an Elliptic System

Abstract

The existence and uniqueness of the positive solution for the generalized Lotka-Volterra competition model for several competing species Δu^i + u^i(a - g(u¹, ..., uN^)) = 0 in Ω , u^i = 0 on ∂Ω , for i = 1, ...,N were investigated. The techniques used in this paper are elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.