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 ) Δ u ( t − 1 ) ] + q ( t ) u ( t ) = λ f ( t , u ( t ) ) , t ∈ Z [ 1 , T ] , u ( 0 ) = u ( T ) , p ( 0 ) Δ u ( 0 ) = p ( T ) Δ u ( 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.