Positive solution of fourth order ordinary differential equation with four-point boundary conditions

In this work, the authors consider the fourth order nonlinear ordinary differential equation u((4))(t) = f (t, u (t)), 0 < t < 1, with the four-point boundary conditions u (0) = u (1) = 0, au ''(xi(1)) - bu'''(xi(1)) = 0, cu ''(xi(2)) + du'''(xi(2)) = 0, where 0 <= xi(1) < xi(2) <= 1. By means of the upper and lower solution method and fixed point theorems, some results on the existence of positive solutions to the above four-point boundary value problem are obtained. (C) 2005 Elsevier Ltd. All rights reserved.