Positive solutions of BVPs for third-order nonlinear difference systems

In this paper, we consider the following discrete system boundary value problems: Δ3u1(k)f1(k,u1(k),u2(k))=0, kε[O,T], Δ3u2(k)f2(k,u1(k),u2(k))=0, kε[O,T], with the Dirichlet boundary condition u1(0)=u1(1)=u1(T+3)=0=u2(0)=u2(1)=u2(T+3} Some sufficient conditions are obtained for the existence of one or two positive solutions to the above system by using a nonlinear alternative of Leray-Schauder type and Krasnoselʹskiiʹs fixed point theorem in a cone.