Uniqueness of positive solutions for semilinear elliptic systems

We prove uniqueness of positive solutions for the system Δu=−λf (v), Δv =−μg(u) in Ω, u = v =0 on∂Ω, where Ω is a bounded domain in RN, f, g :R+ →R+ and f (x) ∼ xp, g(x) ∼ xq at ∞ for some positive numbers p, q with pq < 1.  2005 Elsevier Inc. All rights reserved