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International Journal of Differential Equations
Volume 2015, Article ID 263837, 10 pages
http://dx.doi.org/10.1155/2015/263837
Research Article

Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory

Laboratory LMA, Department of Mathematics, University of Annaba, Elhadjar, 23 Annaba, Algeria

Received 5 July 2015; Accepted 27 August 2015

Academic Editor: Jaume Giné

Copyright © 2015 Amar Makhlouf and Lilia Bousbiat. 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 provide sufficient conditions for the existence of periodic solutions of the polynomial third order differential system ,  ,  and  , where , , and are polynomials in the variables , , and of degree with being periodic functions, is a real number, and is a small parameter.