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

In this paper, a kind of Liénard equation with two deviating arguments of the formx″(t)+f(x(t))x′(t)+g1(t,x(t-τ1(t)))+g2(t,x(t-τ2(t)))=p(t)x″(t)+f(x(t))x′(t)+g1(t,x(t-τ1(t)))+g2(t,x(t-τ2(t)))=p(t)is considered. We derive some new sufficient conditions for checking uniqueness of T-periodic solutions of this equation. By using coincidence degree theory, we also establish some new results on the existence and uniqueness of T-periodic solutions for this equation, which are new and complement previously known results.