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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⊂RN is a bounded domain with C2-boundary ∂Ω,1<p(x),q(x)∈C1(Ω¯) are functions. The operator −Δp(x) u=−div(∣∇u∣p(x)−2∇u) is called the p(x)-Laplacian. When α, β, δ, γ satisfy some suitable conditions, we prove the existence of positive solution via sub-supersolution arguments without assuming sign conditions on the functions h1 and h2

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