A numerical method to obtain positive solution for classes of sublinear semipositone systems

Using a numerical method based on sub-super solution, we will obtain positive solution to the coupled-system of boundary value problems of the form-Δu(x)=λf(x,u,v),x∈Ω,-Δv(x)=λg(x,u,v),x∈Ω,u(x)=0=v(x),x∈∂Ω,where f, g are C1 functions with at least one of f(x0, 0, 0) or g(x0, 0, 0) being negative for some x0 ∈ Ω (semipositone).