Positive solutions of fourth-order four-point boundary value problems with p-Laplacian operator

In this paper, we consider the existence of positive solutions for the singular fourth-order p-Laplacian equation [phi(p)(u ''(t))]'' = f(t, u(t)), 0 < t < 1, with the four-point boundary conditions u(0) = 0, u (1) = au(xi), u ''(0) = 0, u ''(1) = bu ''(eta), where phi(p)(t) = vertical bar t vertical bar(p-2)t, p > 1, 0 < xi, eta < 1, f is an element of C((0, 1) x (0, +infinity), [0, +infinity)) may be singular at t = 0 and/or 1 and u = 0. By using the upper and lower solution method and fixed-point theorems, the existence of positive solutions to the above the boundary value problem is obtained. (c) 2007 Elsevier Inc. All rights reserved.