Asymptotic stability and periodic solutions of vector Liénard equations

Abstract

We prove the asymptotic stability of the equilibrium solution of a class of vector Liénard 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 Liénard equations.

Cited by in corpus (1)

• Nonlocal transformations of the Generalized Liénard type equations and dissipative Ermakov-Milne-Pinney systems