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.