Existence of positive solutions of a class of discrete difference systems

In this paper, we consider the existence of positive solutions of aclass of discrete difference systems$$aligned&-Delta^2 u(t-1)=lambda f(v(t)), t in [1,T]_mathbb{Z},&-Delta^2v(t-1)=lambda g(u(t)), t in [1,T]_mathbb{Z},&~u(0)=u(T+1)=0,&~v(0)=v(T+1)=0endaligned$$where $f,gin C([0,infty),mathbb{R})$, $lambda$ is a positiveparameter. We prove the existence of a large positive solution for$lambda$ large enough under suitable assumptions on $f$ and $g$.The proof of our main result is based upon the Schauder's fixedpoint theorem.