Boundary Value Problems
Volume 2010 (2010), Article ID 626054, 18 pages
doi:10.1155/2010/626054
Research Article

Existence of Positive Solutions of Nonlinear Second-Order Periodic Boundary Value Problems

Ruyun Ma, Chenghua Gao, and Ruipeng Chen

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

Received 31 August 2010; Revised 30 October 2010; Accepted 8 November 2010

Academic Editor: Irena Rachůnková

Copyright © 2010 Ruyun Ma et al. 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

This paper is devoted to study the existence of periodic solutions of the second-order equation 𝑥 = 𝑓 ( 𝑡 , 𝑥 ) , where 𝑓 is a Carathéodory function, by combining a new expression of Green's function together with Dancer's global bifurcation theorem. Our main results are sharp and improve the main results by Torres (2003).