Existence and uniqueness of periodic solutions for a kind of Rayleigh equation with finitely many deviating arguments

In this paper, we consider a kind of Rayleigh equation with finitely many deviating arguments of the form x″+f(t,x′(t))+∑k=1ngk(t,x(t−τk(t)))=p(t). By using the coincidence degree theory, we establish the results on the existence and uniqueness of periodic solutions for the above equation. The results we obtained include and improve the results existing in the literature.