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 Delta(3)u(n) + a(n)f(n, u(w(n))) = 0, 0 less than or equal to n less than or equal to T, satisfying u(n) = phi(n), n(1) less than or equal to n less than or equal to 1, and u(n) = psi(n), T + 3 less than or equal to n less than or equal to n(2), with phi(0) = phi(1) psi(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. (C) 2002 Elsevier Science Ltd. All rights reserved.