New results on the periodic solutions for a kind of Rayleigh equation with two deviating arguments

With the help of the continuation theorem of the coincidence degree, a priori estimates, and differential inequalities, the authors make a further investigation of a class of Rayleigh equation with two deviating arguments of the form x″+f(x′(t))+g1(t,x(t−τ1(t)))+g2(t,x(t−τ2(t)))=p(t).x″+f(x′(t))+g1(t,x(t−τ1(t)))+g2(t,x(t−τ2(t)))=p(t). Some new results on the existence of TT-periodic solutions for such a system are established. Our work generalizes and improves some earlier publications.