Periodic solutions for a type of neutral system with variable parameters

In this paper, we firstly analyze some properties of the linear difference operator[Ax](t)=x(t) -C(t)x(t -τ),where C(t) is a n×n matrix function, and then using Mawhin's continuation theorem, a first-order neutral functional differential system is studied. Some new results on the existence and stability of periodic solutions are obtained. The results are related to the deviating arguments τ and µ. Meanwhile, the approaches to estimate a prior bounds of periodic solutions are different from the corresponding ones of the known literature.