Positive solutions of boundary value problems for third-order functional difference equations

The existence of positive solutions are established for the third-order functional difference equation Δ3u(n) + a(n)f(n, u(w(n))) = 0, 0 ≤ n ≤ T, satisfying u(n) = φ(n), n1 ≤ n ≤ 1, and u(n) = ψ(n), T + 3 ≤ n ≤ n2, with φ(0) = φ(1) = ψ(T + 3) = 0. The results in this paper generalize and substantially improve recent work by Agarwal and Henderson on boundary value problems related to third-order difference equations.