On the existence of a unique periodic solution to a Liénard type p-Laplacian non-autonomous equation

In this work, we investigate the following Liénard type pp-Laplacian non-autonomous equation: (φp(x′(t)))′+f(x(t))x′(t)+g(t,x(t))=e(t).(φp(x′(t)))′+f(x(t))x′(t)+g(t,x(t))=e(t). Some criteria for guaranteeing the existence and uniqueness of periodic solutions of this equation are given by using the Manásevich–Mawhin continuation theorem and some new techniques. Our results are new and extend some known results from the literature. In the last section, two illustrative examples will be provided to demonstrate the applications of our results.