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

In this paper, we consider a kind of Rayleigh equation with two deviating arguments of the form x″+f(t,x′(t))+g1(t,x(t−τ1(t)))+g2(t,x(t−τ2(t)))=p(t).x″+f(t,x′(t))+g1(t,x(t−τ1(t)))+g2(t,x(t−τ2(t)))=p(t). By using the coincidence degree theory, we establish new results on the existence and uniqueness of periodic solutions for the above equation.