- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2011 (2011), Article ID 370982, 14 pages
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.
- J. Diblík, M. Růžičková, and E. Schmeidel, “Asymptotically periodic solutions of Volterra difference equations,” Tatra Mountains Mathematical Publications, vol. 43, pp. 43–61, 2009.
- 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.
- S. N. Elaydi, An Introduction to Difference Equations, Undergraduate Texts in Mathematics, Springer, New York, NY, USA, 3rd edition, 2005.
- 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.
- 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.
- 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.
- 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.
- I. Győri and D. W. Reynolds, “On asymptotically periodic solutions of linear discrete Volterra equations,” Fasciculi Mathematici, no. 44, pp. 53–67, 2010.
- 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.
- 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.
- 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.
- S. Stević, “Periodicity of max difference equations,” Utilitas Mathematica, vol. 83, pp. 69–71, 2010.
- S. Stević and K. S. Berenhaut, “The behavior of positive solutions of a nonlinear second-order difference equation ,” Abstract and Applied Analysis, vol. 2008, Article ID 653243, 8 pages, 2008.
- J. Musielak, Wstep Do Analizy Funkcjonalnej, PWN, Warszawa, Poland, 1976.
- E. Zeidler, Nonlinear Functional Analysis and Its Applications. I, Springer, New York, NY, USA, 1986.
- 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.
- 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.