Uniqueness for a Class of Singular Semilinear Elliptic Systems

Abstract

We prove the existence, uniqueness and asymptotic behavior of solutions to the elliptic system −Δu = a(x)f(u,v) in Ω, −Δv = b(x)g(u,v) in Ω, u = v = 0 on ∂Ω, where Ω is a bounded domain in R^N with smooth boundary ∂Ω,a,b: Ω → (0,∞), and f,g: (0,∞) × (0,∞) → (0,∞) are allowed to be singular at 0 and non-monotone.