On the linear and nonlinear discrete second-order Neumann boundary value problems

By construct the spectrum of the linear eigenvalue problem, we are concerned with the global structure of the set of sign-changing solutions to the discrete second-order Neumann boundary value problem-Δ[p(t-1)Δu(t-1)]+q(t)u(t)=ra(t)f(u(t)),t∈[1,T]Z,Δu(0)=Δu(T)=0.Furthermore, we obtain the existence of the sign-changing solutions of the above nonlinear problem.