Existence of solutions for a third order differential equation with integral boundary conditions

In this paper, we consider the following third order differential equation (phi(u ''))' + f(t, u(t), u'(t), u ''(t)) = 0, 0 < t < 1, subject to the following integral boundary conditions u(0) = 0, u'(0) - k(1)u ''(0) = integral(1)(0)h(1)(u(s))ds, u'(1) + k(2)u ''(1) = integral(1)(0)h(2)(u(s))ds, where f : [0, 1] x R-3 -> R and h(i) : R -> R are continuous and k(1), k(2) > phi, (u) is a continuous and strictly increasing function with phi(0) = 0, phi (R) = R, where R = (-infinity, +infinity). The existence result to the above boundary value problem is obtained by applying the method of upper and lower solutions and Leray-Schauder degree theory. (c) 2007 Elsevier Ltd. All rights reserved.