Nonnegative solutions for nonlinear elliptic systems

In this paper, we show that the semilinear elliptic systems of the form − u− μ v = g(v), − v −λ u = f (u), x ∈ Ω, u = v = 0, x∈ ∂Ω, (0.1) possess at least one nonnegative nontrivial solution pair (u, v) ∈ H1 0 (Ω)×H1 0 (Ω), where Ω is a smooth bounded domain in RN. © 2006 Elsevier Inc. All rights reserved.