Fourth-order problems with nonlinear boundary conditions

We develop anew method of lower and upper solutions for a fourth-order nonlinear boundary value problem where the differential equation has dependence on all lower-order derivatives. Our boundary conditions are nonlinear. We will assume the functions that define the nonlinear boundary conditions are either monotone or nonmonotone. As a result we obtain existence principles which improve recent results in the literature. (C) 2004 Elsevier B.V. All rights reserved.