Abstract and Applied Analysis
Volume 2012 (2012), Article ID 909387, 17 pages
Research Article

The Existence and Uniqueness of Periodic Solutions for Some Nonlinear 𝑛 th-Order Differential Equations

1College of Mathematics and Computer Science, Hunan University of Arts and Science, Changde, Hunan 415000, China
2College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, China

Received 15 December 2011; Accepted 19 March 2012

Academic Editor: Gabriel Turinici

Copyright © 2012 Qiyuan Zhou and Shuhua Gong. 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.


The nonlinear 𝑛 th-order differential equations are considered. By using inequality techniques and coincidence degree theory, some criteria are obtained to guarantee the existence and uniqueness of 𝑇 -periodic solutions for the equations. The obtained results are also valid and new for the problem discussed in the previous literature. Moreover, two illustrative examples are provided to illustrate the effectiveness of our results.