In this paper, by using the theory of Fourier series and continuation theorem of coincidence degree theory, we study a kind of second-order n-Dimensional neutral functional differential system with deviating arguments as follows: ((d2)/(dt2)) (x(t) - Cx(t - r)) + ((d)/(dt))gradF(x(t)) + gradG(x(t - τ (t))) = p(t). Some new results on the existence of periodic solutions are obtained. The interesting thing is that the matrix C is not required to be symmetric. Therefore, the results of this paper inprove and extend some known results in recent literature. But, the methods to estimate a priori bounds of periodic solutions are different from the corresponding ones of the past.
LI Xiaojing, ZHOU Youming, LU Shiping. On the Existence of Periodic Solutions for a Kind of Second-order n-dimensional Neutral Functional Differential System[J]. Acta Mathematicae Applicatae Sinica, 2011, 34(3): 560-573.