Focal boundary value problems for singular difference equations

Solutions are shown to exist for the boundary value problem Δnu(m) + f(m, u, Δu, ..., Δn−2u) = 0, m “0, ..., T”, satisfying focal boundary conditions, where f(m, y1, ..., yn−1) is singular at yi = 0, 1 ≤ i ≤ n. The techniques involve concavity properties, iterations, and a fixed point theorem for mappings which are decreasing with respect to a cone in a Banach space.