Existence and uniqueness of periodic solutions for a kind of Liénard equation with a deviating argument

Abstract

In this work, we use the coincidence degree theory to establish new results on the existence and uniqueness of $T$-periodic solutions for a kind of Liénard equation with a deviating argument of the form

$$x^{″}\left(t\right)+f\left(x\left(t\right)\right)x^{\prime }\left(t\right)+g(t,x(t-\tau \left(t\right)))=p\left(t\right)\text{.}$$