About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 237036, 12 pages
http://dx.doi.org/10.1155/2012/237036
Research Article

Bounded Positive Solutions for a Third Order Discrete Equation

1Liaoning Normal University, Department of Mathematics, Dalian, Liaoning 116029, China
2Dalian Hongwen Middle School, Dalian, Liaoning 116029, China
3Gyeongsang National University, Department of Mathematics and RINS, Jinju 660-701, Republic of Korea
4Dong-A University, Department of Mathematics, Pusan 614-714, Republic of Korea

Received 21 February 2012; Accepted 12 April 2012

Academic Editor: Josef Diblík

Copyright © 2012 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. R. P. Agarwal, S. R. Grace, and D. O'Regan, “Nonoscillatory solutions for discrete equations,” Computers & Mathematics with Applications, vol. 45, no. 6–9, pp. 1297–1302, 2003. View at Publisher · View at Google Scholar
  2. 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.
  3. J. Baštinec, L. Berezansky, J. Diblík, and Z. Šmarda, “A final result on the oscillation of solutions of the linear discrete delayed equation Δx(n)=p(n)x(nk) with a positive coefficient,” Abstract and Applied Analysis, vol. 2011, Article ID 586328, 28 pages, 2011. View at Publisher · View at Google Scholar
  4. J. Baštinec and J. Diblík, “Subdominant positive solutions of the discrete equation Δu(k+n)=p(k)u(k),” Abstract and Applied Analysis, vol. 2004, no. 6, pp. 461–470, 2004. View at Publisher · View at Google Scholar
  5. J. Baštinec and J. Diblík, “Remark on positive solutions of discrete equation Δu(k+n)=p(k)u(k),” Nonlinear Analysis, vol. 63, no. 5–7, pp. e2145–e2151, 2005.
  6. J. Baštinec, J. Diblík, and Z. Šmarda, “Existence of positive solutions of discrete linear equations with a single delay,” Journal of Difference Equations and Applications, vol. 16, no. 9, pp. 1047–1056, 2010. View at Publisher · View at Google Scholar
  7. J. F. Cheng and Y. M. Chu, “Oscillation theorem for second-order difference equations,” Taiwanese Journal of Mathematics, vol. 12, no. 3, pp. 623–633, 2008.
  8. S. S. Cheng and W. T. Patula, “An existence theorem for a nonlinear difference equation,” Nonlinear Analysis, vol. 20, no. 3, pp. 193–203, 1993. View at Publisher · View at Google Scholar
  9. W. T. Li, X. L. Fan, and C. K. Zhong, “On unbounded positive solutions of second-order difference equations with a singular nonlinear term,” Journal of Mathematical Analysis and Applications, vol. 246, no. 1, pp. 80–88, 2000. View at Publisher · View at Google Scholar
  10. M. Migda and J. Migda, “Asymtotic properties of solutions of second-order neutral difference equations,” Nonlinear Analysis, vol. 63, pp. 789–799, 2005.
  11. J. Yan and B. Liu, “Asymptotic behavior of a nonlinear delay difference equation,” Applied Mathematics Letters, vol. 8, pp. 1–5, 1995.