Boundary Value Problems
Volume 2011 (2011), Article ID 192156, 11 pages
doi:10.1155/2011/192156
Research Article

Existence and Uniqueness of Periodic Solution for Nonlinear Second-Order Ordinary Differential Equations

Jian Zu

College of Mathematics, Jilin University, Changchun 130012, China

Received 22 May 2010; Accepted 6 March 2011

Academic Editor: Kanishka Perera

Copyright © 2011 Jian Zu. 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 periodic solutions for nonlinear second-order ordinary differential problem 𝑥 ′ ′ + 𝑓 ( 𝑡 , 𝑥 , 𝑥 ) = 0 . By constructing upper and lower boundaries and using Leray-Schauder degree theory, we present a result about the existence and uniqueness of a periodic solution for second-order ordinary differential equations with some assumption.