Positive solutions for nonlinear discrete second-order boundary value problems with parameter dependence

In this paper, we consider the nonlinear discrete boundary value problem{−Δ[p(t−1)Δu(t−1)]+q(t)u(t)=λf(t,u(t)),t∈Z[1,T],u(0)=u(T),p(0)Δu(0)=p(T)Δu(T), where λ is a positive parameter. By using the fixed point index theory, the criteria of the existence, multiplicity and nonexistence of positive solutions are established in terms of different values of λ.