On the existence of positive solutions for a class of (p(x),q(x)p(x),q(x))-Laplacian system

We consider the system {−Δp(x)u=λ1a(x)f(v)+μ1α(x)h(u),in Ω,−Δq(x)v=λ2b(x)g(u)+μ2β(x)γ(v),in Ω,u=0=v,on ∂Ω, where p(x)∈C1(RN)p(x)∈C1(RN) is a radial symmetric function such that sup|∇p(x)|<∞sup|∇p(x)|<∞, 1