Boundary Value Problems
Volume 2011 (2011), Article ID 297578, 17 pages
doi:10.1155/2011/297578
Research Article

Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary Conditions

Ruyun Ma and Tianlan Chen

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 5 May 2010; Accepted 7 July 2010

Academic Editor: Daniel Franco

Copyright © 2011 Ruyun Ma and Tianlan Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the existence of positive solutions of the following fourth-order boundary value problem with integral boundary conditions, u(4)(t)=f(t,u(t),u′′(t)), t∈(0,1), u(0)=∫01g(s)u(s)ds, u(1)=0, u′′(0)=∫01h(s)u′′(s)ds, u′′(1)=0, where f:[0,1]×[0,+∞)×(-∞,0]→[0,+∞) is continuous, g,h∈L1[0,1] are nonnegative. The proof of our main result is based upon the Krein-Rutman theorem and the global bifurcation techniques.