Positive Solutions for a System of Neumann Boundary Value Problems of Second-Order Difference Equations Involving Sign-Changing Nonlinearities

In this paper, we study the existence of positive solutions for the system of second-order difference equations involving Neumann boundary conditions: -Δ2u1(t-1)=f1(t,u1(t),u2(t)), t∈[1,T]Z, -Δ2u2(t-1)=f2(t,u1(t),u2(t)), t∈[1,T]Z, Δui(0)=Δui(T)=0, i=1,2, where T>1 is a given positive integer, Δu(t)=u(t+1)-u(t), and Δ2u(t)=Δ(Δu(t)). Under some appropriate conditions for our sign-changing nonlinearities, we use the fixed point index to establish our main results.