Consider the multiplicity of solutions to the nonlinear second-order discrete problems with minimum and maximum: Δ 2 u ( k − 1 ) = f ( k , u ( k ) , Δ u ( k ) ) , k ∈ T , min { u ( k ) : k ∈ T ^ } = A , max ⁡ { u ( k ) : k ∈ T ^ } = B , where f : T × ℝ 2 → ℝ ,     a , b ∈ ℕ are fixed numbers satisfying b ≥ a + 2 ,     and     A , B ∈ ℝ are satisfying B > A ,     T = { a + 1 , … , b − 1 } ,     T ^ = { a , a + 1 , … , b − 1 , b } .