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In this work, we investigate the following Rayleigh type equation: x″(t)+f(x′(t))+g(t,x(t))=e(t). Some criteria for guaranteeing the existence of asymptotically stable (in the sense of Lyapunov) periodic solutions of this equation is presented by using Mawhin’s continuation theorem, Floquet theory, Lyapunov stability theory and some analysis techniques. Moreover, an example is provided to illustrate...
.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,...
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