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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 246723, 7 pages
http://dx.doi.org/10.1155/2013/246723
Research Article

On Some Symmetric Systems of Difference Equations

1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, 60200 Brno, Czech Republic
2Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech Republic
3Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Beograd, Serbia
4Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, Serbia
5Department of Mathematics, King Abdulaziz University, Jeddah 21859, Saudi Arabia

Received 22 December 2012; Accepted 12 February 2013

Academic Editor: Norio Yoshida

Copyright © 2013 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. L. Berg and S. Stević, “On the asymptotics of some difference equations,” Journal of Difference Equations and Applications, vol. 18, no. 5, pp. 785–797, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B. D. Iričanin and S. Stević, “Some systems of nonlinear difference equations of higher order with periodic solutions,” Dynamics of Continuous, Discrete & Impulsive Systems A, vol. 13, no. 3-4, pp. 499–507, 2006. View at Zentralblatt MATH · View at MathSciNet
  3. B. Iričanin and S. Stević, “Eventually constant solutions of a rational difference equation,” Applied Mathematics and Computation, vol. 215, no. 2, pp. 854–856, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. N. Kruse and T. Nesemann, “Global asymptotic stability in some discrete dynamical systems,” Journal of Mathematical Analysis and Applications, vol. 235, no. 1, pp. 151–158, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. W. Liu, X. Yang, S. Stević, and B. Iričanin, “Part metric and its applications to cyclic discrete dynamical systems,” Abstract and Applied Analysis, vol. 2011, Article ID 534974, 16 pages, 2011. View at Publisher · View at Google Scholar
  6. G. Papaschinopoulos and C. J. Schinas, “On a system of two nonlinear difference equations,” Journal of Mathematical Analysis and Applications, vol. 219, no. 2, pp. 415–426, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. G. Papaschinopoulos and C. J. Schinas, “On the behavior of the solutions of a system of two nonlinear difference equations,” Communications on Applied Nonlinear Analysis, vol. 5, no. 2, pp. 47–59, 1998. View at Zentralblatt MATH · View at MathSciNet
  8. G. Papaschinopoulos and C. J. Schinas, “Invariants for systems of two nonlinear difference equations,” Differential Equations and Dynamical Systems, vol. 7, no. 2, pp. 181–196, 1999. View at Zentralblatt MATH · View at MathSciNet
  9. G. Papaschinopoulos and C. J. Schinas, “Invariants and oscillation for systems of two nonlinear difference equations,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 46, no. 7, pp. 967–978, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. G. Papaschinopoulos and C. J. Schinas, “Oscillation and asymptotic stability of two systems of difference equations of rational form,” Journal of Difference Equations and Applications, vol. 7, no. 4, pp. 601–617, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. G. Papaschinopoulos and C. J. Schinas, “Global asymptotic stability and oscillation of a family of difference equations,” Journal of Mathematical Analysis and Applications, vol. 294, no. 2, pp. 614–620, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. G. Stefanidou, G. Papaschinopoulos, and C. J. Schinas, “On a system of two exponential type difference equations,” Communications on Applied Nonlinear Analysis, vol. 17, no. 2, pp. 1–13, 2010. View at Zentralblatt MATH · View at MathSciNet
  13. S. Stević, “Global stability and asymptotics of some classes of rational difference equations,” Journal of Mathematical Analysis and Applications, vol. 316, no. 1, pp. 60–68, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S. Stević, “On positive solutions of a (k+1)-th order difference equation,” Applied Mathematics Letters, vol. 19, no. 5, pp. 427–431, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. S. Stević, “Existence of nontrivial solutions of a rational difference equation,” Applied Mathematics Letters, vol. 20, no. 1, pp. 28–31, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. Stević, “Nontrivial solutions of a higher-order rational difference equation,” Mathematical Notes, vol. 84, no. 5-6, pp. 718–724, 2008. View at Publisher · View at Google Scholar
  17. S. Stević, “On a system of difference equations,” Applied Mathematics and Computation, vol. 218, no. 7, pp. 3372–3378, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. S. Stević, “On a solvable rational system of difference equations,” Applied Mathematics and Computation, vol. 219, no. 6, pp. 2896–2908, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  19. S. Stević, “On a third-order system of difference equations,” Applied Mathematics and Computation, vol. 218, no. 14, pp. 7649–7654, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. S. Stević, “On some solvable systems of difference equations,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 5010–5018, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. A. C. Thompson, “On certain contraction mappings in a partially ordered vector space,” Proceedings of the American Mathematical Society, vol. 14, pp. 438–443, 1963. View at Zentralblatt MATH · View at MathSciNet
  22. X. Yang, M. Yang, and H. Liu, “A part-metric-related inequality chain and application to the stability analysis of difference equation,” Journal of Inequalities and Applications, vol. 2007, Article ID 19618, 9 pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. I. Yalcinkaya, “On the global asymptotic stability of a second-order system of difference equations,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 860152, 12 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. N. Yalcinkaya and C. Çinar, “Global asymptotic stability of a system of two nonlinear difference equations,” Fasciculi Mathematici, no. 43, pp. 171–180, 2010. View at Zentralblatt MATH · View at MathSciNet
  25. I. Yalcinkaya, C. Cinar, and D. Simsek, “Global asymptotic stability of a system of difference equations,” Applicable Analysis, vol. 87, no. 6, pp. 677–687, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet