Stability properties and existence theorems of pseudo almost periodic solutions of linear Volterra difference equations

The purpose of this article is to discuss the existence of pseudo almost periodic solutions of linear Volterra equation: x ( n + 1 ) = A ( n ) x ( n ) + ∑ s = - ∞ n F ( n , s ) x ( s ) + p ( n ) , n ∈ Z , by using an exponentially stable of the zero solution, which is equivalent to the exponential b...

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Bibliographic Details
Published inAdvances in Difference Equations Vol. 2012; no. 1; pp. 1 - 11
Main Author Hamaya, Yoshihiro
Format Journal Article
LanguageEnglish
Published Cham Springer Science and Business Media LLC 09.05.2012
Springer International Publishing
Springer Nature B.V
BioMed Central Ltd
Subjects
Algebra and Number Theory
Analysis
Applied Mathematics
Classifications
Difference and Functional Equations
Difference equations
Equivalence
Existence theorems
Functional Analysis
Kernels
Mathematics
Mathematics and Statistics
Metal oxide semiconductors
Ordinary Differential Equations
Partial Differential Equations
Stability
Volterra equations
Difference Equation
Periodic Solution
Periodic Function
Initial Function
Integrodifferential Equation
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Summary:The purpose of this article is to discuss the existence of pseudo almost periodic solutions of linear Volterra equation: x ( n + 1 ) = A ( n ) x ( n ) + ∑ s = - ∞ n F ( n , s ) x ( s ) + p ( n ) , n ∈ Z , by using an exponentially stable of the zero solution, which is equivalent to the exponential behaviors of the resolvent matrix G ( n, m ) as n → ∞ and of some summability of the kernel. AMS (MOS) 2000 Subject classifications: 39A11.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/1687-1847-2012-58