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Let T be an integer with T≥3, and let T:={1,…,T}. We study the existence and uniqueness of solutions for the following two-point boundary value problems of second-order difference systems:Δ2u(t−1)+f(t,u(t))=e(t),t∈T, u(0)=u(T+1)=0, where e:T→â„Ân  and  f:T×â„Ân→â„Ân is a potential function satisfying f(t,⋅)∈C1(â„Ân) and some nonresonance conditions. The proof of the main result is based upon a mini-max theorem.