| 中立型泛函微分方程周期解问题 |
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| 引用本文： | 鲁世平,葛渭高. 中立型泛函微分方程周期解问题[J]. 应用数学和力学, 2002, 23(12): 1269-1275 |
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| 作者姓名： | 鲁世平 葛渭高 |
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| 作者单位： | 1.北京理工大学应用数学系, 北京 100081; |
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| 基金项目： | 国家自然科学基金资助项目 (198710 0 5 )，高校博士点专项基金项目 (19990 0 0 72 2 ) |
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| 摘 要： | 利用Fourier级数理论研究了一类k-阶线性中立型泛函微分方程周期解问题,给出了周期解存在唯一性的充要条件。利用此结果并结合Schauder不动点原理,进一步研究了一类k-阶非线性中立型泛函微分方程,得到了存在周期解的新的结果。这些结果改进和推广了近期文献中的已有结论。
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| 关 键 词： | 中立型泛函微分方程 不动点原理 周期解 |
| 文章编号： | 1000-0887(2002)12-1269-07 |
| 收稿时间： | 2000-09-25 |
| 修稿时间： | 2000-09-25 |
Problem of Periodic Solutions for Neutral Functional Differential Equation |
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| LU Shi_ping ,,GE Wei_gao. Problem of Periodic Solutions for Neutral Functional Differential Equation[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1269-1275 |
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| Authors: | LU Shi_ping GE Wei_gao |
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| Affiliation: | 1.Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, P R China;2.Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241000, P R China |
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| Abstract: | The problem of periodic solutions for a kind of k_th order linear neutral functional differential equation is studied. By using the theory of Fourier expansions, a sufficient and necessary condition to guarantee the existence and uniqueness of periodic solution is obtained. Further, by applying this result and Schauder's fixed point principle, a kind of k_th order nonlinear neutral functional differential equation is investigated, and some new results on existence of the periodic solutions are given as well. These results improve and extend some known results in recent literature. |
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| Keywords: | neutral functional differential equation fixed point principle periodic solution |
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