一类二阶n-维中立型泛函微分系统周期解存在性问题

On the Existence of Periodic Solutions for a Kind of Second-order n-dimensional Neutral Functional Differential System

利用Fourier级数理论和重合度理论研究了一类二阶n-维中立型泛函微分系统d^2/(dt^2)(x(t)-Cx(t-r))+d/(dt)gradF(x(t))+gradG(x(t-τ(t)))=p(t)的周期解问题,得到了周期解存在性的新结论,有意义的是本文的矩阵C仅为一般的实方阵,不必为实对称阵,因而本文的结果改进和推广了已有工作.此外,本文周期解先验界估计方法与已有工作也不同.

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： （d^2）/（dt^2）（x（t） - Cx（t - r）） ＋d/（dt）gradF（x（t）） ＋ gradG（x（t - r（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.