No abstract

In this work, we will be concerned with the following forced Liénard type equation:Under certain assumptions, some new criteria for guaranteeing the existence of asymptotically stable (in the sense of Liapunov) periodic solutions of this equation are presented by applying Manásevich-Mawhin continuation theorem, Floquet theory, Liapunov stability theory and some analysis techniques. Moreover, an example is provided to demonstrate the applications of our results.

In this work, we shall be concerned with the following forced Rayleigh type equation:Under certain assumptions, some criteria for guaranteeing the existence, uniqueness and asymptotic stability (in the Lyapunov sense) of periodic solutions of this equation are presented by applying the Manásevich-Mawhin continuation theorem, Floquet theory, Lyapunov stability theory and some analysis techniques. Moreover, an example is provided to demonstrate the applications of our results.2000 Mathematics subject classification: primary 34K15, 34C25.