Electron. J. Diff. Eqns., Vol. 2006(2006), No. 140, pp. 1-10.

Existence of periodic solution for perturbed generalized Lienard equations

Islam Boussaada, A. Raouf Chouikha

Abstract:
Under conditions of Levinson-Smith type, we prove the existence of a $\tau$-periodic solution for the perturbed generalized Lienard 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.

Show me the PDF file (567K), TEX file, and other files for this article.

Islam Boussaada
LMRS, UMR 6085, Universite de Rouen
Avenue de l'universit&aecute;e, BP.12
76801 Saint Etienne du Rouvray, France
email: islam.boussaada@etu.univ-rouen.fr
A. Raouf Chouikha
Universite Paris 13 LAGA
Villetaneuse 93430, France
email: chouikha@math.univ-paris13.fr

Return to the EJDE web page