On a class of quasilinear systems with sign-changing nonlinearities

We prove existence and nonexistence of positive solutions for the quasilinear system − pu = λa(x)f (u, v) in Ω, − qv = μb(x)g(u, v) in Ω, u = v =0 on∂Ω, where pu = div(|∇u|p−2∇u), qv = div(|∇v|q−2∇v), p, q > 1, Ω is a bounded domain in RN, and the coefficients a(x) and b(x) are allowed to change sign. © 2007 Elsevier Inc. All rights reserved.