An existence result for a class of Kirchhoff type systems via sub and supersolutions method

This paper deals with the existence of positive solutions for the following Kirchhoff type systems {−M1(∫Ω|∇u|pdx)Δpu=λa(x)f(u,v)in  Ω,−M2(∫Ω|∇v|qdx)Δqv=λb(x)g(u,v)in  Ω,u=v=0on  ∂Ω, where Ω is a bounded smooth domain of RN, p,q>1, Mi:R0+→R+, i=1,2 are two continuous and increasing functions, λ is a positive parameter, and a,b∈C(Ω¯). We discuss the existence of a large positive solution for λ large when limt→∞f(t,M[g(t,t)]1q−1)tp−1=0 for every M>0, and limt→∞g(t,t)tq−1=0. In particular, we do not assume any sign conditions on f(0,0) or g(0,0).