无限时滞线性中立型泛函微分方程周期解 (英)

Periodic Solutions of Linear Neutral Functional Differential Equations with Infinite Delay

中文关键词:  线性中立型泛函微分方程  无限时滞  有界解  周期解  充要条件.

英文关键词:linear neutral functional differential equation  infinite delay  bounded solution  periodic solution  necessary and sufficient condition.

中文摘要:

      本文以$C_g$空间为相空间, 证明了具无限时滞$D$算子型线性中立型泛函微分方程存在周期解当且仅当存在有界解, 得到了与以往结论互不包含的结果.

英文摘要:

      In this paper, we chose space $C_g$ as phase space. It had been proved that for linear neutral functional differential equations of $D$-operator type with infinite delay, there was a periodic solution if and only if there was a bounded solution. Our results were different from the ones given in Acta Mathematica Sinica, 4(2000)695-702.