Existence of positive solution for second-order nonlinear discrete system with parameter

This paper is concerned with the following discrete system, Δ 2 u i ( k ) + λ h i ( k ) f i ( u 1 ( k ) , u 2 ( k ) , … , u n ( k ) ) = 0 , k ∈ [ 0 , T ] , i = 1 , 2 … , n , u i ( 0 ) = u i ( T + 2 ) = 0 , i = 1 , 2 , ⋯ , n . By using the theory of the fixed-point index, sufficient conditions are obtained for the existence of positive solution to the above system.