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 ) ) + g 1 ( t , x ( t − τ 1 ( t ) ) ) + g 2 ( t , x ( t − τ 2 ( t ) ) ) = p ( t ) . Some new results on the existence of T -periodic solutions for such a system are established. Our work generalizes and improves some earlier publications.