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)−cx(t−σ))(n)+f(x(t))x′(t)+g(∫−r0x(t+s)dα(s))=p(t). Some new results on the existence of periodic solutions are obtained.