Open Access

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

Advances in Difference Equations20072007:068023

DOI: 10.1155/2007/68023

Received: 4 November 2006

Accepted: 29 January 2007

Published: 13 March 2007


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.


Authors’ Affiliations

Department of Mathematics, Suzhou University


  1. Yoshizawa T: Asymptotically almost periodic solutions of an almost periodic system. Funkcialaj Ekvacioj 1969, 12: 23–40.MATHMathSciNetGoogle 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.2003.10.002MATHMathSciNetView ArticleGoogle 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.MATHMathSciNetView ArticleGoogle Scholar
  5. Elaydi SN: An Introduction to Difference Equations, Undergraduate Texts in Mathematics. 2nd edition. Springer, New York, NY, USA; 1999:xviii+427.View ArticleGoogle Scholar
  6. Elaydi S, Zhang S: Stability and periodicity of difference equations with finite delay. Funkcialaj Ekvacioj 1994,37(3):401–413.MATHMathSciNetGoogle Scholar
  7. Elaydi S, Györi I: Asymptotic theory for delay difference equations. Journal of Difference Equations and Applications 1995,1(2):99–116. 10.1080/10236199508808012MATHMathSciNetView ArticleGoogle 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. 10.1080/10236199908808167MATHMathSciNetView ArticleGoogle 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. 10.1080/1023619031000080844MATHMathSciNetView ArticleGoogle Scholar
  11. Song Y, Baker CTH: Perturbations of Volterra difference equations. Journal of Difference Equations and Applications 2004,10(4):379–397. 10.1080/10236190310001625253MATHMathSciNetView ArticleGoogle 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.MATHMathSciNetView ArticleGoogle 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. 10.1080/1023619021000035836MATHMathSciNetView ArticleGoogle 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.2005.04.001MATHMathSciNetView ArticleGoogle Scholar
  15. Song Y: Almost periodic solutions of discrete Volterra equations. Journal of Mathematical Analysis and Applications 2006,314(1):174–194.MATHMathSciNetView ArticleGoogle 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 MathematicsGoogle Scholar
  17. Zhang S, Liu P, Gopalsamy K: Almost periodic solutions of nonautonomous linear difference equations. Applicable Analysis 2002,81(2):281–301. 10.1080/0003681021000021961MATHMathSciNetView ArticleGoogle Scholar
  18. Zhang C: Almost Periodic Type Functions and Ergodicity. Science Press, Beijing, China; Kluwer Academic, Dordrecht, The Netherlands; 2003:xii+355.MATHView ArticleGoogle 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.View ArticleGoogle Scholar


© Yihong Song. 2007

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