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.