PROBLEM OF PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (12): 1421-1428.

PROBLEM OF PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

鲁世平^1,2, 葛渭高¹

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

收稿日期:2000-09-25 修回日期:2002-06-11 出版日期:2002-12-18 发布日期:2002-12-18
基金资助:
the National Natural Science Foundation of China(19871005);the Research Found for the Doctoral Program of Higher Education of China(1999000722)

PROBLEM OF PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

LU Shi-ping^1,2, GE Wei-gao¹

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

Received:2000-09-25 Revised:2002-06-11 Online:2002-12-18 Published:2002-12-18
Supported by:
the National Natural Science Foundation of China(19871005);the Research Found for the Doctoral Program of Higher Education of China(1999000722)

摘要/Abstract

摘要： The problem of periodic solutions for a kind of kth-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 kth-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.

关键词: neutral functional differential equation, fixed point principle, periodic solution

Abstract: The problem of periodic solutions for a kind of kth-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 kth-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.

Key words: neutral functional differential equation, fixed point principle, periodic solution

中图分类号:

O175.1

鲁世平;葛渭高. PROBLEM OF PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(12): 1421-1428.

LU Shi-ping;GE Wei-gao. PROBLEM OF PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(12): 1421-1428.

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PROBLEM OF PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

PROBLEM OF PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

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