On existence of periodic solutions of a kind of Rayleigh equation with a deviating argument

Existence of periodic solutions for a kind of Rayleigh equation with a deviating argument x″(t)+f(x′(t))+g(t,x(t−τ(t)))=p(t)x″(t)+f(x′(t))+g(t,x(t−τ(t)))=p(t) is studied, and some new results are obtained. Our work generalizes and improves the known results in the literature.