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.