Fifth Mississippi State Conference on Differential Equations and Computational Simulations,
Electron. J. Diff. Eqns., Conf. 10, 2003, pp. 115-122.

### Solutions series for some non-harmonic motion equations A. Raouf Chouikha

Abstract:
We consider the class of nonlinear oscillators of the form

where is a -periodic function, is a function only dependent on , and is a small parameter. We are interested in the periodic solutions with minimal period , when the restoring term is such that and is a trigonometric polynomial with period . By using method based on expanding the solution as a sine power series, we prove the existence of periodic solutions for this perturbed equation.

Published February 28, 2003.
Subject classifications: 34A20.
Key words: power series solution, trigonometric series.

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 A. Raouf Chouikha University of Paris-Nord, Laga, CNRS UMR 7539 Villetaneuse F-93430, France e-mail: chouikha@math.univ-paris13.fr