【摘要】 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.更多还原

【Abstract】 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.更多还原