Periodic Solutions for a Class of p-Laplacian Neutral Functional Differential Equation with Distributed

Mawhin coincidence degree theory and widely function-analysis's knowledge were used to obtain new sufficient condition of periodic solutions for a class of p-Laplacian neutral functional differential equation with distributed as follows:
\left(\varphi_p(x(t)-c x(t-\sigma))^\prime\right)^\prime+f\left(t, x^\prime(t)\right)+\beta(t) g\left(\int_-r^0 x(t+s) \mathrmd m(s)\right)=e(t)
The results improved the related reports in the literatures, and the coefficient β(t) was proposed.