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

Abstract

In this paper, a kind of Lienard equation with multiple deviating arguments of the form $$x''(t)+f(x(t))x'(t)+\sum_{k=1}^{n}g_{k}(t,x(t-\tau_{k}(t)))=p(t)$$ is considered. By using coincidence degree theory, some criteria are obtained to guarantee the existence and uniqueness of periodic solutions of this equation. The obtained results are also valid and new for the problem discussed in the previous literature.