,THE EXISTENCE AND UNIQUENESS OF A POSITIVE SOLUTION OF AN ELLIPTIC SYSTEM

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The existence and uniqueness of the positive solution for the generalized Lotka-Volterra competition model for several competing species Δui+ui(a-g(u1,…,un))=0 in Ω,ui=0 on бΩ 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.
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