Copyright © 2010 Guoju Ye and Xiuli Li. 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

By the notation and monotone convergence theorem of Henstock-Kurzweil integral, we investigate the existence of continuous solutions for the second order boundary value problems with integral boundary conditions in which the nonlinearities f(t,x(t)) are allowed to have the singularities in t and are not Lebesgue integrable.