Existence of positive solutions for a class of p(x)-Laplacian systems ✩

We mainly consider the system ⎧⎨⎩ − p(x)u = λf (x, v) in Ω, − p(x)v = λg(x, u) in Ω, u = v =0 on ∂Ω, where Ω ⊂ RN is a bounded domain, p(x) is a function which satisfies some conditions, − p(x)u = −div(|∇u|p(x)−2∇u) is called p(x)-Laplacian. We give the existence of positive solutions under some conditions. In particular, we do not assume radial symmetric conditions on the system. © 2006 Elsevier Inc. All rights reserved