A Spectrum Relation of Almost Periodic Solution of Second Order Scalar Functional Differential Equations with Piecewise Constant Argument

In this paper, the spectrum relation of almost periodic solution for the equation （x（t） ＋px（t - 1））＂ = qx（[t]） ＋ f（Q is investigated. Although this has been discussed in an article, some counterexamples are constructed to show that some part of the spectrum inclusion in that article is not correct....

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2011-11, Vol.27 (11), p.2275-2284
Main Authors: Wang, Li, Yuan, Rong, Zhang, Chuan Yi
Format: Article
Language:English
Subjects:
Banach spaces
Construction
Differential equations
Inclusions
Mathematical analysis
Mathematics
Mathematics and Statistics
Scalars
Studies
二阶
标量
概周期解
泛函微分方程
逐段常变量
频谱
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Summary:In this paper, the spectrum relation of almost periodic solution for the equation （x（t） ＋px（t - 1））＂ = qx（[t]） ＋ f（Q is investigated. Although this has been discussed in an article, some counterexamples are constructed to show that some part of the spectrum inclusion in that article is not correct. The key point which causes such problem is found out. A new statement is formulated and proved.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-011-8392-8