Electronic Journal of Differential Equations,
Conf. 10 (2002), pp. 115--122. 

Title: Solutions series for some non-harmonic motion equations

Author: A. Raouf  Chouikha (Univ. of Paris-Nord, Laga, France)
 
Abstract: 
 We consider the class of nonlinear oscillators of the form
 \begin{gather*}
 {d^2 u\over{dt^2}} + f(u)  = \epsilon g(t)  \\
 u(0) = a_0, \quad u'(0) = 0,
 \end{gather*}
 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.
Math Subject Classifications: 34A20.
Key Words: Power series solution; trigonometric series.