一类高阶中立型方程的周期解

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基金项目: 云南省自然科学研究基金资助课题(97A012G)

Periodic Solutions of a Class of Higher Order Neutral Type Equations

摘要: 利用Fourier级数理论讨论了一类高阶中立型方程的周期解问题。所得结果改进了司建国(应用数学和力学,第17卷1期:关于高阶常系数中立型方程周期解的讨论)的主要结果,即将该文定理1的条件|b₀|<1/2改为|b₀|≠1,从而该文的其它定理也可相应得到改进。
- 周期解 /
- 中立型方程 /
- Fourier级数
Abstract: In this paper, by using the theory of Fourier series, some necessary and sufficient conditions of existence and uniqueness of periodic solutions of a class of higher order neutral type equations are obtained. The main results by Shi Jianguo in "Discussion on the periodic solutions for linear equation of neutral type with constant coefficients" are improved, i.e., the condition |b₀|≠1 instead of the condition |b₀|<1/2 of Theorem 1 by Shi Jianguo is given. Other theorems by Shi are rebuilt and improved according to the new assumption.
- periodic solution /
- neutral type equation /
- Fourier series

[1]	司建国.关于高阶常系数线性中立型方程周期解的讨论[J].应用数学和力学,1996,17(1):29～37.
[2]	章毅,张毅.关于二阶常系数线性中立型方程的周期解[J].数学学报,1990,33(4):517～520.
[3]	曹进德等,一类二阶中立型方程的周期解[J].纯粹数学与应用数学,1995,11(增刊):102～106.