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Periodic and Almost Periodic Solutions of Functional Difference Equations with Finite Delay

Abstract

For periodic and almost periodic functional difference equations with finite delay, the existence of periodic and almost periodic solutions is obtained by using stability properties of a bounded solution.

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References

  1. Yoshizawa T: Asymptotically almost periodic solutions of an almost periodic system. Funkcialaj Ekvacioj 1969, 12: 23–40.

    MATH  MathSciNet  Google Scholar 

  2. Agarwal RP: Difference Equations and Inequalities, Monographs and Textbooks in Pure and Applied Mathematics. Volume 228. 2nd edition. Marcel Dekker, New York, NY, USA; 2000:xvi+971.

    Google Scholar 

  3. Baker CTH, Song Y: Periodic solutions of discrete Volterra equations. Mathematics and Computers in Simulation 2004,64(5):521–542. 10.1016/j.matcom.2003.10.002

    Article  MATH  MathSciNet  Google Scholar 

  4. Cuevas C, Pinto M: Asymptotic properties of solutions to nonautonomous Volterra difference systems with infinite delay. Computers & Mathematics with Applications 2001,42(3–5):671–685.

    Article  MATH  MathSciNet  Google Scholar 

  5. Elaydi SN: An Introduction to Difference Equations, Undergraduate Texts in Mathematics. 2nd edition. Springer, New York, NY, USA; 1999:xviii+427.

    Book  Google Scholar 

  6. Elaydi S, Zhang S: Stability and periodicity of difference equations with finite delay. Funkcialaj Ekvacioj 1994,37(3):401–413.

    MATH  MathSciNet  Google Scholar 

  7. Elaydi S, Györi I: Asymptotic theory for delay difference equations. Journal of Difference Equations and Applications 1995,1(2):99–116. 10.1080/10236199508808012

    Article  MATH  MathSciNet  Google Scholar 

  8. Elaydi S, Murakami S, Kamiyama E: Asymptotic equivalence for difference equations with infinite delay. Journal of Difference Equations and Applications 1999,5(1):1–23. 10.1080/10236199908808167

    Article  MATH  MathSciNet  Google Scholar 

  9. Györi I, Ladas G: Oscillation Theory of Delay Differential Equations, Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, NY, USA; 1991:xii+368.

    Google Scholar 

  10. Song Y, Baker CTH: Perturbation theory for discrete Volterra equations. Journal of Difference Equations and Applications 2003,9(10):969–987. 10.1080/1023619031000080844

    Article  MATH  MathSciNet  Google Scholar 

  11. Song Y, Baker CTH: Perturbations of Volterra difference equations. Journal of Difference Equations and Applications 2004,10(4):379–397. 10.1080/10236190310001625253

    Article  MATH  MathSciNet  Google Scholar 

  12. Agarwal RP, O'Regan D, Wong PJY: Constant-sign periodic and almost periodic solutions of a system of difference equations. Computers & Mathematics with Applications 2005,50(10–12):1725–1754.

    Article  MATH  MathSciNet  Google Scholar 

  13. Hamaya Y: Existence of an almost periodic solution in a difference equation with infinite delay. Journal of Difference Equations and Applications 2003,9(2):227–237. 10.1080/1023619021000035836

    Article  MATH  MathSciNet  Google Scholar 

  14. Ignatyev AO, Ignatyev OA: On the stability in periodic and almost periodic difference systems. Journal of Mathematical Analysis and Applications 2006,313(2):678–688. 10.1016/j.jmaa.2005.04.001

    Article  MATH  MathSciNet  Google Scholar 

  15. Song Y: Almost periodic solutions of discrete Volterra equations. Journal of Mathematical Analysis and Applications 2006,314(1):174–194.

    Article  MATH  MathSciNet  Google Scholar 

  16. Song Y, Tian H: Periodic and almost periodic solutions of nonlinear Volterra difference equations with unbounded delay. to appear in Journal of Computational and Applied Mathematics

  17. Zhang S, Liu P, Gopalsamy K: Almost periodic solutions of nonautonomous linear difference equations. Applicable Analysis 2002,81(2):281–301. 10.1080/0003681021000021961

    Article  MATH  MathSciNet  Google Scholar 

  18. Zhang C: Almost Periodic Type Functions and Ergodicity. Science Press, Beijing, China; Kluwer Academic, Dordrecht, The Netherlands; 2003:xii+355.

    Book  MATH  Google Scholar 

  19. Yoshizawa T: Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Applied Mathematical Sciences. Volume 14. Springer, New York, NY, USA; 1975:vii+233.

    Book  Google Scholar 

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Correspondence to Yihong Song.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Song, Y. Periodic and Almost Periodic Solutions of Functional Difference Equations with Finite Delay. Adv Differ Equ 2007, 068023 (2007). https://doi.org/10.1155/2007/68023

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