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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 316093, 7 pages
http://dx.doi.org/10.1155/2014/316093
Research Article

Multiple Positive Periodic Solutions for a Functional Difference System

College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, China

Received 20 January 2014; Accepted 12 May 2014; Published 22 May 2014

Academic Editor: Samir Saker

Copyright © 2014 Yue-Wen Cheng and Hui-Sheng Ding. 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. B. Liu, “The existence and uniqueness of positive periodic solutions of Nicholson-type delay systems,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3145–3151, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B. Liu and S. Gong, “Periodic solution for impulsive cellar neural networks with time-varying delays in the leakage terms,” Abstract and Applied Analysis, vol. 2013, Article ID 701087, 10 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. O. Alzabut and C. Tunç, “Existence of periodic solutions for Rayleigh equations with state-dependent delay,” Electronic Journal of Differential Equations, vol. 77, pp. 1–8, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. O. Alzabut, “Existence of periodic solutions for a type of linear difference equations with distributed delay,” Advances in Difference Equations, p. 2012, article 53, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H.-S. Ding and J. G. Dix, “Multiple Periodic Solutions for Discrete Nicholson's Blowflies Type System,” Abstract and Applied Analysis, vol. 2014, Article ID 659152, 6 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J. G. Dix, S. Padhi, and S. Pati, “Multiple positive periodic solutions for a nonlinear first order functional difference equation,” Journal of Difference Equations and Applications, vol. 16, no. 9, pp. 1037–1046, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. W. Long, X. J. Zheng, and L. Li, “Existence of periodic solutions for a class of functional integral equations,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 57, pp. 1–11, 2012. View at Google Scholar · View at MathSciNet
  8. Y. N. Raffoul, “Positive periodic solutions of nonlinear functional difference equations,” Electronic Journal of Differential Equations, vol. 55, pp. 1–8, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Y. N. Raffoul and C. C. Tisdell, “Positive periodic solutions of functional discrete systems and population models,” Advances in Difference Equations, no. 3, pp. 369–380, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. E. Braverman and S. H. Saker, “Permanence, oscillation and attractivity of the discrete hematopoiesis model with variable coefficients,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 10, pp. 2955–2965, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. E. Braverman and S. H. Saker, “Periodic solutions and global attractivity of a discrete delay host macroparasite model,” Journal of Difference Equations and Applications, vol. 16, no. 7, pp. 789–806, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. E. Braverman and S. H. Saker, “On the Cushing-Henson conjecture, delay difference equations and attenuant cycles,” Journal of Difference Equations and Applications, vol. 14, no. 3, pp. 275–286, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. E. Braverman and S. H. Saker, “On a difference equation with exponentially decreasing nonlinearity,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 147926, 17 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. E. M. Elabbasy and S. H. Saker, “Periodic solutions and oscillation of discrete non-linear delay population dynamics model with external force,” IMA Journal of Applied Mathematics, vol. 70, no. 6, pp. 753–767, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  15. S. H. Saker, “Qualitative analysis of discrete nonlinear delay survival red blood cells model,” Nonlinear Analysis: Real World Applications, vol. 9, no. 2, pp. 471–489, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. H. Saker, “Periodic solutions, oscillation and attractivity of discrete nonlinear delay population model,” Mathematical and Computer Modelling, vol. 47, no. 3-4, pp. 278–297, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. Z. C. Hao, T. J. Xiao, and J. Liang, “Multiple positive periodic solutions for delay differential system,” Discrete Dynamics in Nature and Society, vol. 2009, Article ID 239209, 18 pages, 2009. View at Publisher · View at Google Scholar
  18. R. I. Avery and J. Henderson, “Two positive fixed points of nonlinear operators on ordered Banach spaces,” Communications on Applied Nonlinear Analysis, vol. 8, no. 1, pp. 27–36, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. R. W. Leggett and L. R. Williams, “Multiple positive fixed points of nonlinear operators on ordered Banach spaces,” Indiana University Mathematics Journal, vol. 28, no. 4, pp. 673–688, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet