On the existence of periodic solutions for a kind of high-order neutral functional differential equation

By using the coincidence degree theory of Mawhin, we study a kind of high-order neutral functional differential equation with distributed delay as follows: ( x ( t ) − c x ( t − σ ) ) ( n ) + f ( x ( t ) ) x ′ ( t ) + g ( ∫ − r 0 x ( t + s ) d α ( s ) ) = p ( t ) . Some new results on the existence of periodic solutions are obtained.