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 form x ″ ( t ) + f ( x ( t ) ) x ′ ( t ) + g 1 ( t , x ( t - τ 1 ( t ) ) ) + g 2 ( t , x ( t - τ 2 ( 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.