A remark on uniqueness of large solutions for elliptic systems of competitive type

We prove that the semilinear system Delta u = a(x)u(p)v(q), Delta v = b(x)u(r)v(s) in a smooth bounded domain Omega subset of R-N has a unique positive solution with the boundary condition u = v = +infinity on partial derivative Omega, provided that p, s > 1, q, r > 0 and (p - 1)(s - 1) - qr > 0. The main novelty is imposing a growth on the possibly singular weights a(x), b(x) near partial derivative Omega, rather than requiring them to have a precise asymptotic behavior. (C) 2006 Elsevier Inc. All rights reserved.