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·
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.
出处
《应用数学和力学》
EI
CSCD
北大核心
2002年第12期1269-1275,共7页
Applied Mathematics and Mechanics
基金
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 )
关键词
中立型泛函微分方程
不动点原理
周期解
neutral functional differential equation
fixed point principle
periodic solution