Abstract and Applied Analysis

Multiple Positive Periodic Solutions for a Functional Difference System

Yue-Wen Cheng and Hui-Sheng Ding

Full-text: Open access

Abstract

We obtain two existence results about multiple positive periodic solutions for a class of functional difference system. Two examples are given to illustrate our results.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 316093, 7 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425047800

Digital Object Identifier
doi:10.1155/2014/316093

Mathematical Reviews number (MathSciNet)
MR3214419

Citation

Cheng, Yue-Wen; Ding, Hui-Sheng. Multiple Positive Periodic Solutions for a Functional Difference System. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 316093, 7 pages. doi:10.1155/2014/316093. https://projecteuclid.org/euclid.aaa/1425047800


Export citation

References

  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Y. N. Raffoul, “Positive periodic solutions of nonlinear functional difference equations,” Electronic Journal of Differential Equations, vol. 55, pp. 1–8, 2002.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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. \endinput