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 inActa mathematica Sinica. English series Vol. 27; no. 11; pp. 2275 - 2284
Main Authors Wang, Li, Yuan, Rong, Zhang, Chuan Yi
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.11.2011
Springer Nature B.V
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
34K14
Neutral delay-differential equation
spectrum
almost periodicity
piecewise constant argument
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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.
Bibliography:11-2039/O1
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.
Neutral delay-differential equation, piecewise constant argument, almost periodicity, spectrum
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-011-8392-8