Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 140, pp. 1-10.
Title: Existence of periodic solution for perturbed
generalized Lienard equations
Authors: Islam Boussaada (Univ. de Rouen, France)
A. Raouf Chouikha (Univ. Paris 13, France)
Abstract:
Under conditions of Levinson-Smith type, we prove the existence
of a $\tau$-periodic solution for the perturbed generalized Li\'enard equation
$$
u''+\varphi(u,u')u'+\psi(u)=\epsilon\omega(\frac{t}{\tau},u,u')
$$
with periodic forcing term. Also we deduce sufficient condition for existence
of a periodic solution for the equation
$$ u''+\sum_{k=0}^{2s+1} p_k(u){u'}^k=\epsilon\omega(\frac{t}{\tau},u,u').
$$
Our method can be applied also to the equation
$$
u''+[u^2+(u+u')^2-1]u'+u=\epsilon\omega(\frac{t}{\tau},u,u').
$$
The results obtained are illustrated with numerical examples.
Submitted May 15, 2006. Published November 1, 2006.
Math Subject Classifications: 34C25.
Key Words: Perturbed systems; Lienard equation; periodic solution.