Let T > 5 be an integer, T = {1, 2,..., T}. We are concerned with the global structure of positive solutions set of the discrete second-order boundary value problems Δ²u(t - 1) + rm(t)f(u(t)) 0, t ∈, u(0) = u(T + 1) = 0, where r ∈ R is a parameter, m : T → R changes its sign and m(t) ≠ 0 for t ∈ T.