Positive solutions for a class of p-Laplacian systems with multiple parameters

Consider the system−Δpu=λ1f(v)+μ1h(u)in Ω,−Δqv=λ2g(u)+μ2γ(v)in Ω,u=0=von ∂Ω, where Δsz=div(|∇z|s−2∇z)Δsz=div(|∇z|s−2∇z), s>1s>1, λ1λ1, λ2λ2, μ1μ1 and μ2μ2 are nonnegative parameters, and Ω   is a bounded domain in RNRN with smooth boundary ∂Ω  . We prove the existence of a large positive solution for λ1+μ1λ1+μ1 and λ2+μ2λ2+μ2 large whenlimx→∞f(M[g(x)]1/q−1)xp−1=0 for every M>0M>0, limx→∞h(x)xp−1=0 and limx→∞γ(x)xq−1=0. In particular, we do not assume any sign conditions on f(0)f(0), g(0)g(0), h(0)h(0) or γ(0)γ(0). We also discuss a multiplicity results when f(0)=g(0)=h(0)=γ(0)=0f(0)=g(0)=h(0)=γ(0)=0.