International Journal of Differential Equations
Volume 2011 (2011), Article ID 916279, 21 pages
http://dx.doi.org/10.1155/2011/916279
Research Article

Periodic Solutions for a Class of 𝑛 -th Order Functional Differential Equations

Bing Song,1,2 Lijun Pan,3 and Jinde Cao1

1Department of Mathematics, Southeast University, Nanjing 210096, China
2JiangSu Institute of Economic Trade Technology, Nanjing 211168, China
3School of Mathematics, Jia Ying University, Meizhou Guangdong, 514015, China

Received 10 May 2011; Accepted 14 July 2011

Academic Editor: Peiguang Wang

Copyright © 2011 Bing Song 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

We study the existence of periodic solutions for n-th order functional differential equations 𝑥 ( 𝑛 ) ∑ ( 𝑡 ) = 𝑛 − 1 𝑖 = 0 𝑏 𝑖 [ 𝑥 ( 𝑖 ) ( 𝑡 ) ] 𝑘 + 𝑓 ( 𝑥 ( 𝑡 − 𝜏 ( 𝑡 ) ) ) + 𝑝 ( 𝑡 ) . Some new results on the existence of periodic solutions of the equations are obtained. Our approach is based on the coincidence degree theory of Mawhin.