On Stability of Periodic Solutions of Lienard Type Equations

Abstract

We use the Floquet theory to analyze the stability of periodic solutions of Lienard type equations under the asymptotic linear growth of restoring force in this paper. We find that the existence and the stability of periodic solutions are determined primarily by asymptotic behavior of damping term. For special type of Lienard equation, the uniqueness and stability of periodic solutions are obtained. Furthermore, the sharp rate of exponential decay of the stable periodic solutions is determined under suitable conditions imposed on restoring force.