New Results on Existence of Asymptotically Stable Periodic Solutions of a Forced Liénard Type Equation

摘要

In this work, we will be concerned with the following forced Liénard type equation: $$x^{prime prime} (t) + f(x(t))x^{prime} (t) + g(t, x(t)) = e(t)$$ . 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.