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

We prove that the semilinear system u = a(x)upvq , v = b(x)ur vs in a smooth bounded domain Ω ⊂ RN has a unique positive solution with the boundary condition u = v =+∞on ∂Ω, 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 ∂Ω, rather than requiring them to have a precise asymptotic behavior. © 2006 Elsevier Inc. All rights reserved