On the existence of periodic solution of perturbed generalized Liénard equations

Details On the existence of periodic solution of perturbed generalized Liénard equations On the existence of periodic solution of perturbed generalized Liénard equations

2006-10-27

arxiv.org/abs/math/0610847v1

Mathematics

Classical Analysis and ODEs

15 pages, 5 figures

Scientific paper

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'). The results obtained are illustrated with numerical examples.

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