A remark on the existence of positive solutions for variable exponent elliptic systems

In this article, we consider the system of differential equations-Δp(x)u=λp(x)[a(x)uα(x)vγ(x)+h1(x)]inΩ,-Δq(x)v=λq(x)[b(x)uδ(x)vβ(x)+h2(x)]inΩ,u=v=0on∂Ω,where Ω⊂RNΩ⊂RN is a bounded domain with C2-boundary ∂Ω,1