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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 −∆u = λ 1 f (v) + µ 1 h(u) in Ω −∆v = λ 2 g(u) + µ 2 γ(v) in Ω u = 0 = v on ∂Ω where −∆ is the Laplacian operator λ 1 , λ 2 , µ 1 , µ 2 are nonnegative parameters, and Ω is a bounded region in R n , with smooth(More)
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 −∆u(x) = λf (x, u, v) x ∈ Ω −∆v(x) = λg(x, u, v) x ∈ Ω u(x) = 0 = v(x) x ∈ ∂Ω where f , g are C 1 functions with at least one of f (x 0 , 0, 0) or g(x 0 , 0, 0) being negative for some x 0 ∈ Ω (semipositone).