Uniqueness of positive solutions for semilinear elliptic systems

We prove uniqueness of positive solutions for the systemΔu=−λf(v),Δv=−μg(u)inΩ,u=v=0on∂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.