# On the existence of periodic solution of perturbed generalized Li\'enard equations

@article{Boussaada2006OnTE, title={On the existence of periodic solution of perturbed generalized Li\'enard equations}, author={Islam Boussaada and Abd Raouf Chouikha}, journal={arXiv: Classical Analysis and ODEs}, year={2006} }

Under conditions of Levinson-Smith type, we prove the existence of a $\tau$-periodic solution for the perturbed generalized Li\'enard equation u''+\phi(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…

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