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
$$\displaylines{ {d^2 u\over{dt^2}} + f(u) = \epsilon g(t) \cr u(0) = a_0, \quad u'(0) = 0, }$$
where $g(t)$ is a $2T$-periodic function, $f$ is a function only dependent on $u$, and $\epsilon $ is a small parameter. We are interested in the periodic solutions with minimal period $2T$, when the restoring term $f$ is such that $f(u)=\omega ^2u+u^2$ and $g$ is a trigonometric polynomial with period $2T=\frac{\pi}{\omega}$. 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

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