Existence of positive solutions for elliptic systems with nonstandard p(x)p(x)-growth conditions via sub-supersolution method

We mainly consider the system {−△p(x)u=f(v)in Ω,−△p(x)v=g(u)in Ω,u=v=0on ∂Ω, where p(x)∈C1(RN)p(x)∈C1(RN) is a radial symmetric function which satisfies sup|∇p(x)|<∞sup|∇p(x)|<∞ and 1