Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 470181, 16 pages
http://dx.doi.org/10.1155/2014/470181
Research Article

On Positive Solutions and Mann Iterative Schemes of a Third Order Difference Equation

1Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China
2Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
3Department of Mathematics, Dong-A University, Pusan 614-714, Republic of Korea

Received 14 October 2013; Accepted 16 December 2013; Published 28 January 2014

Academic Editor: Zhi-Bo Huang

Copyright © 2014 Zeqing Liu 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. M. H. Abu-Risha, “Oscillation of second-order linear difference equations,” Applied Mathematics Letters, vol. 13, no. 1, pp. 129–135, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  2. R. P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, NY, USA, 2nd edition, 2000.
  3. R. P. Agarwal and J. Henderson, “Positive solutions and nonlinear eigenvalue problems for third-order difference equations,” Computers & Mathematics with Applications, vol. 36, no. 10-12, pp. 347–355, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. Andruch-Sobiło and M. Migda, “On the oscillation of solutions of third order linear difference equations of neutral type,” Mathematica Bohemica, vol. 130, no. 1, pp. 19–33, 2005. View at Google Scholar · View at MathSciNet
  5. Z. Došlá and A. Kobza, “Global asymptotic properties of third-order difference equations,” Computers & Mathematics with Applications, vol. 48, no. 1-2, pp. 191–200, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  6. S. R. Grace and G. G. Hamedani, “On the oscillation of certain neutral difference equations,” Mathematica Bohemica, vol. 125, no. 3, pp. 307–321, 2000. View at Google Scholar · View at MathSciNet
  7. J. Cheng, “Existence of a nonoscillatory solution of a second-order linear neutral difference equation,” Applied Mathematics Letters, vol. 20, no. 8, pp. 892–899, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  8. L. Kong, Q. Kong, and B. Zhang, “Positive solutions of boundary value problems for third-order functional difference equations,” Computers & Mathematics with Applications, vol. 44, no. 3-4, pp. 481–489, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  9. I. Y. Karaca, “Discrete third-order three-point boundary value problem,” Journal of Computational and Applied Mathematics, vol. 205, no. 1, pp. 458–468, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  10. W.-T. Li and J. P. Sun, “Existence of positive solutions of BVPs for third-order discrete nonlinear difference systems,” Applied Mathematics and Computation, vol. 157, no. 1, pp. 53–64, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  11. W.-T. Li and J.-P. Sun, “Multiple positive solutions of BVPs for third-order discrete difference systems,” Applied Mathematics and Computation, vol. 149, no. 2, pp. 389–398, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  12. Z. Liu, M. Jia, S. M. Kang, and Y. C. Kwun, “Bounded positive solutions for a third order discrete equation,” Abstract and Applied Analysis, vol. 2012, Article ID 237036, 12 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  13. Z. Liu, S. M. Kang, and J. S. Ume, “Existence of uncountably many bounded nonoscillatory solutions and their iterative approximations for second order nonlinear neutral delay difference equations,” Applied Mathematics and Computation, vol. 213, no. 2, pp. 554–576, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  14. Z. Liu, Y. Xu, and S. M. Kang, “Bounded oscillation criteria for certain third order nonlinear difference equations with several delays and advances,” Computers & Mathematics with Applications, vol. 61, no. 4, pp. 1145–1161, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  15. M. Migda and J. Migda, “Asymptotic properties of solutions of second-order neutral difference equations,” Nonlinear Analysis: Theory, Methods and Applications, vol. 63, no. 5–7, pp. e789–e799, 2005. View at Publisher · View at Google Scholar · View at Scopus
  16. N. Parhi, “Non-oscillation of solutions of difference equations of third order,” Computers & Mathematics with Applications, vol. 62, no. 10, pp. 3812–3820, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  17. N. Parhi and A. Panda, “Nonoscillation and oscillation of solutions of a class of third order difference equations,” Journal of Mathematical Analysis and Applications, vol. 336, no. 1, pp. 213–223, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  18. S. H. Saker, “New oscillation criteria for second-order nonlinear neutral delay difference equations,” Applied Mathematics and Computation, vol. 142, no. 1, pp. 99–111, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  19. S. H. Saker, “Oscillation of third-order difference equations,” Portugaliae Mathematica, vol. 61, no. 3, pp. 249–257, 2004. View at Google Scholar · View at MathSciNet
  20. 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 MathSciNet
  21. X. H. Tang, “Bounded oscillation of second-order delay difference equations of unstable type,” Computers & Mathematics with Applications, vol. 44, no. 8-9, pp. 1147–1156, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  22. J. Yan and B. Liu, “Asymptotic behavior of a nonlinear delay difference equation,” Applied Mathematics Letters, vol. 8, no. 6, pp. 1–5, 1995. View at Google Scholar · View at Scopus
  23. Z. G. Zhang and Q. L. Li, “Oscillation theorems for second-order advanced functional difference equations,” Computers & Mathematics with Applications, vol. 36, no. 6, pp. 11–18, 1998. View at Publisher · View at Google Scholar · View at MathSciNet