Existence of periodic solutions for a type of linear difference equations with distributed delay

By employing primary algebraic techniques, we establish a necessary and sufficient condition for the existence of periodic solutions for a type of linear difference equations with distributed delay of the form Δ x ( n ) = ∑ k = - d 0 Δ k ζ ( n + 1 , k - 1 ) x ( n + k - 1 ) , n ≥ 1 . (*) Our approach...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2012; no. 1; pp. 1 - 14
Main Author Alzabut, Jehad O
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 03.05.2012
Springer Nature B.V
BioMed Central Ltd
Subjects
Adjoints
Algebra
Analysis
Classification
Construction
Delay
Difference and Functional Equations
Difference equations
Differential
Dynamic Equations
Functional Analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Oscillation of Difference
Partial Differential Equations
periodic solutions
distributed delay
adjoint
difference equations
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Summary:By employing primary algebraic techniques, we establish a necessary and sufficient condition for the existence of periodic solutions for a type of linear difference equations with distributed delay of the form Δ x ( n ) = ∑ k = - d 0 Δ k ζ ( n + 1 , k - 1 ) x ( n + k - 1 ) , n ≥ 1 . (*) Our approach is based on constructing an adjoint equation for (*) and proving that (*) and its adjoint equation have the same number of linearly independent periodic solutions. AMS Subject Classification: 39A11.
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ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/1687-1847-2012-53