Existence and uniqueness of solutions for a fourth-order boundary value problem

In this paper, we study the fourth-order two-point boundary value problem x '''' (t) - f (t, x(t), x' (t), x '' (t), x ''' (t)) = 0, t is an element of (0, 1), x (0) = x' (1) = 0, ax '' (0) - bx ''' (0) = 0, cx '' (1) + dx ''' (1) = 0. By means of lower and upper solution method, growth conditions on the nonlinear term f which guarantee the existence of solutions for the above boundary value problem are given. In particular, we obtain the uniqueness of the solution by imposing a monotone condition of the term f. (C) 2008 Elsevier Ltd. All rights reserved,