Boundary value problems for functional difference equations Original Research Article

Solutions are obtained for the functional difference equation, Δ2x(t − 1) = f(t, xt−1, Δx(t − 1)), 1 ≤ t ≤ T + 1, satisfying the initial condition, x(s) = φ(s), −N ≤ s ≤ 0, and the boundary condition, x(T + 2) = A. The methods involve the Leray-Schauder Alternative.