A Cooperative Biological Model with Combined Self-limitation and Cooperation Terms

The non-existence and existence of the positive solution for the generalized cooperation biological model for two species of animals . Δu + u(a + g(u,v)) = 0 in Ω Δw + v(d + h(u, v)) = 0 in Ω u = v = o on ∂Ω 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. © SAS International Publications.