On existence of periodic solutions of Rayleigh equation of retarded type

Existence of periodic solutions for a kind of non-autonomous Rayleigh equations of retarded type x ″ ( t ) + f ( t , x ′ ( t - σ ) ) + 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.