Uniqueness of positive solutions for a class of semipositone elliptic systems

We consider the system -Delta u = lambda f(v); x is an element of Omega -Delta v = mu g(u); x is an element of Omega u = 0 = v; x is an element of delta Omega where Omega is a ball in R-N, N >= 1, and delta Omega is its boundary, lambda, mu are positive parameters, and f, g are smooth functions that are negative at the origin and f(x) similar to x(p) and g(x) similar to x(q) for large x for some p, q >= 0 with pq < 1. We establish the uniqueness of positive solutions when the parameters lambda and mu are large. (c) 2006 Elsevier Ltd. All rights reserved.