About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2011 (2011), Article ID 370982, 14 pages
http://dx.doi.org/10.1155/2011/370982
Research Article

Weighted Asymptotically Periodic Solutions of Linear Volterra Difference Equations

1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, 66237 Brno, Czech Republic
2Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech Republic
3Department of Mathematics, University of Žilina, 01026 Žilina, Slovakia
4Faculty of Electrical Engineering, Institute of Mathematics, Poznań University of Technology, 60965 Poznań, Poland

Received 16 January 2011; Accepted 17 March 2011

Academic Editor: Elena Braverman

Copyright © 2011 Josef Diblík et al. 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.

Linked References

  1. J. Diblík, M. Růžičková, and E. Schmeidel, “Asymptotically periodic solutions of Volterra difference equations,” Tatra Mountains Mathematical Publications, vol. 43, pp. 43–61, 2009. View at Zentralblatt MATH
  2. R. P. Agarwal, Difference Equations and Inequalities, vol. 228 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2nd edition, 2000. View at Zentralblatt MATH
  3. S. N. Elaydi, An Introduction to Difference Equations, Undergraduate Texts in Mathematics, Springer, New York, NY, USA, 3rd edition, 2005.
  4. V. L. Kocić and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, vol. 256 of Mathematics and Its Applications, Kluwer Academic, Dordrecht, The Netherlands, 1993.
  5. J. A. D. Appleby, I. Győri, and D. W. Reynolds, “On exact convergence rates for solutions of linear systems of Volterra difference equations,” Journal of Difference Equations and Applications, vol. 12, no. 12, pp. 1257–1275, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. S. Elaydi and S. Murakami, “Uniform asymptotic stability in linear Volterra difference equations,” Journal of Difference Equations and Applications, vol. 3, no. 3-4, pp. 203–218, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. I. Győri and L. Horváth, “Asymptotic representation of the solutions of linear Volterra difference equations,” Advances in Difference Equations, vol. 2008, Article ID 932831, 22 pages, 2008. View at Publisher · View at Google Scholar
  8. I. Győri and D. W. Reynolds, “On asymptotically periodic solutions of linear discrete Volterra equations,” Fasciculi Mathematici, no. 44, pp. 53–67, 2010.
  9. Y. Song and C. T. H. Baker, “Admissibility for discrete Volterra equations,” Journal of Difference Equations and Applications, vol. 12, no. 5, pp. 433–457, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. L. Berg and S. Stević, “Periodicity of some classes of holomorphic difference equations,” Journal of Difference Equations and Applications, vol. 12, no. 8, pp. 827–835, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. S. Stević, “On global periodicity of a class of difference equations,” Discrete Dynamics in Nature and Society, vol. 2007, Article ID 23503, 10 pages, 2007. View at Zentralblatt MATH
  12. S. Stević, “Periodicity of max difference equations,” Utilitas Mathematica, vol. 83, pp. 69–71, 2010.
  13. S. Stević and K. S. Berenhaut, “The behavior of positive solutions of a nonlinear second-order difference equation xn=f(xn2)/g(xn1),” Abstract and Applied Analysis, vol. 2008, Article ID 653243, 8 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. J. Musielak, Wstep Do Analizy Funkcjonalnej, PWN, Warszawa, Poland, 1976.
  15. E. Zeidler, Nonlinear Functional Analysis and Its Applications. I, Springer, New York, NY, USA, 1986.
  16. J. Diblík, E. Schmeidel, and M. Růžičková, “Asymptotically periodic solutions of Volterra system of difference equations,” Computers & Mathematics with Applications, vol. 59, no. 8, pp. 2854–2867, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. J. Diblík, E. Schmeidel, and M. Růžičková, “Existence of asymptotically periodic solutions of system of Volterra difference equations,” Journal of Difference Equations and Applications, vol. 15, no. 11-12, pp. 1165–1177, 2009. View at Zentralblatt MATH