2T-Periodic Solution for m Order Neutral Type Differential Equations With Time Delays
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摘要: 研究m阶常系数线性多时滞中立型方程的周期解,讨论了2T周期解的存在性和唯一性,得到了2T周期解存在唯一若干新的充分必要条件。所得主要结果适用性更广。它包括了许多相关文献的结果为其特例,推广、改进了这些文献的主要结果。可对所研究的中立型方程周期解存在的大量情形作出判断,而这些情形用其他文献的结果是无法判断的。换言之,对方程(1),主要结果是最一般化的,用同样的方法已不可能得到更好的结果。Abstract: Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied.Existence and uniqueness of 2T-periodic solutions for the equation were discussed by using the method of Fourier series.Some new necessary and sufficient conditions of existence and uniqueness of 2T-periodic solutions for the equation are obtained.The main result is used widely.It contains results in some correlation paper for its special case,improves and extends the main results in them.Existence of periodic solution for the equation in larger number of particular case can be checked by using the result,but cannot be checked in another paper.In other words,the main result in this paper is most generalized for(1),the better result by using the same method.
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Key words:
- neutral type equation /
- 2T-periodic solution /
- Fourier series
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