Uniqueness of Nonnegative Solutions for Semipositone Problems on Exterior Domains

We consider the problem −Δu = λK(|x|)f(u), x∈Ω u=0 if |x|=r0 u→0 as |x|→∞, where λ is a positive parameter, Δu = div(∇u)is the Laplacian of u, Ω = {x ∈ Rn; n \u3e 2,|x| \u3e r0}, K ∈ C1([r0,∞),(0,∞)) is such that lim r→∞ K(r) = 0 and f ∈ C1([0,∞),R) is a concave function which is sublinear at ∞ and f(0) \u3c 0. We establish the uniqueness of nonnegative radial solutions when λ is large