Entire positive solution to the system of nonlinear elliptic equations

The second-order nonlinear elliptic system - Δu = f₁ (x)u^α + g₁(x)u^-β + h₁(x)u^γP(v), - Δv = f₂ (x)v^α + g₂(x)v^-β + h₂(x)v^γP(u) with 0 < α, β, γ < 1, is considered in Rdbl;^N. Under suitable hypotheses on functions f_i, g_i, h_i (i = 1,2), and P, it is shown that this system possesses an entire positive solution (u,v) ∈ ℂ_loc^2,θ (ℝ^N) × ℂ_loc^2,θ (ℝ^N) (0 < θ < 1) such that both u and v are bounded below and above by positive constant multiples of x ^2-N for all x ≥ 1.