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International Journal of Differential Equations
Volume 2012 (2012), Article ID 406835, 13 pages
http://dx.doi.org/10.1155/2012/406835
Research Article

Existence of Periodic Solutions to Nonlinear Differential Equations of Third Order with Multiple Deviating Arguments

Department of Mathematics, Faculty of Sciences, Yüzüncü Yıl University, 65080 Van, Turkey

Received 12 May 2012; Accepted 19 July 2012

Academic Editor: D. D. Ganji

Copyright © 2012 Cemil Tunç. 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 establish certain new sufficient conditions which guarantee the existence of periodic solutions for a nonlinear differential equation of the third order with multiple deviating arguments. Using the Lyapunov functional approach, we prove a specific theorem and provide an example to illustrate the theoretical analysis in this work and the effectiveness of the method utilized here.