Asymptotic stability and periodic solutions of vector Liénard equations

Details Asymptotic stability and periodic solutions of vector Liénard equations Asymptotic stability and periodic solutions of vector Liénard equations

2010-08-18

arxiv.org/abs/1008.3118v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We prove the asymptotic stability of the equilibrium solution of a class of
vector Li\'enard equations by means of LaSalle invariance principle. The key
hypothesis consists in assuming that the intersections of the manifolds in
$\{\dot V = 0\}$ be isolated. We deduce an existence theorem for periodic
solutions of periodically perturbed vector Li\'enard equations.

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