Existence and uniqueness of positive solutions of semilinear elliptic systems

A study was conducted to answer the question of existence and uniqueness for positive solutions of the semilinear elliptic system with homogeneous Dirichlet data -Δu = g(v) in Ω, -Δv = f(u) in Ω, u = v = 0 on ∂Ω (equation 1.1), where Ω⊂Rn(n≥1) denotes a bounded domain of class C2,α, α∈(0,1] and f,g satisfying the given hypothesis. The study focused in the case where f is superlinear or sublinear at 0 and ∞ while g is sublinear or superlinear at 0 and ∞.