Skip to content


  • Research Article
  • Open Access

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

Advances in Difference Equations20072007:068023

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.


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Periodic Solution


Authors’ Affiliations

Department of Mathematics, Suzhou University, Suzhou, China


  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

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.