一类中立型泛函微分系统周期解存在性问题  

On the Existence of Periodic Solutions to a Class of Neutral Functional Differential Systems

作　　者：鲁世平[1] 李亚林[2] 

机构地区：[1]南京财经大学应用数学系,南京210046 [2]安徽师范大学数学系,芜湖241000

出　　处：《数学学报（中文版）》2007年第6期1231-1242,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(10371006);教育部科学技术重点项目(207047);安徽省自然科学基金(050460103);安徽省教育厅自然科学重点基金(2005kj031ZD)

摘　　要：首先对线性差分算子M:[Mx](t)=z(t)-Cx(t-r)的性质进行了研究,在此基础上利用Mawhin重合度拓展定理研究了一类具偏差变元的中立型泛函微分系统的周期解问题,得到了周期解存在性的新结论.本文的矩阵C仅为一般的实方阵,不必为实对称阵,因而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相同.In this paper, the authors analyse some properties of the linear difference operator M ： [Mxl（t） = x（t） - Cx（t - r）, and then, by employing the continuation theorem of coincidence degree principle developed by Mawhin, a class of neutral functional differential systems with deviating arguments is studied. Some new results on the existence of periodic solutions are obtained. The significance of this paper is that the matrix C is not required to be symmetric. Therefore, the results of this paper improve and extend some known results in the recent literature. Moreover, the methods to estimate a priori bounds of periodic solutions are different from the corresponding ones of the past.

关 键 词：重合度拓展定理 中立型微分系统 偏差变元 

分 类 号：O175.14[理学—数学]