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Mathematical Problems in Engineering
Volume 2015, Article ID 735758, 7 pages
http://dx.doi.org/10.1155/2015/735758
Research Article

Multiplicity of Periodic Solutions for Third-Order Nonlinear Differential Equations

1Department of Mathematics, Hunan First Normal University, Changsha, Hunan 410205, China
2Department of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China

Received 29 November 2014; Revised 16 March 2015; Accepted 20 March 2015

Academic Editor: Alexander Klimenko

Copyright © 2015 Xuxin Yang 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 third-order nonlinear differential equations. The method of proof relies on Schauder’s fixed point theorem applied in a novel way, where the original equation is transformed into second-order integrodifferential equation through a linear integral operator. Finally, examples are presented to illustrate applications of the main results.