Uniqueness of positive solutions for a class of elliptic systems

In this article, we consider uniqueness of positive radial solutions to the elliptic system Δu + a(|x|)f (u, v) = 0, Δv+b(|x|)g(u, v) = 0, subject to the Dirichlet boundary condition on the open unit ball in RN (N 2). Our uniqueness results applies to, for instance, f (u,v) = uqvp, g(u, v) = upvq , p, q > 0, p +q <1 or more general cases. © 2005 Elsevier Inc. All rights reserved.