Skip to main content

On the Difference equation xn+ = ax n - bx n /(cx x - dxn-1)

Abstract

We investigate some qualitative behavior of the solutions of the difference equation xn+ = ax n - bx n /(cx x - dxn-1), n = 0,1,..., where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants.

[1234567891011121312345678910111213]

References

  1. 1.

    Camouzis E, DeVault R, Papaschinopoulos G: On the recursive sequence. Advances in Difference Equations 2005,2005(1):31–40. 10.1155/ADE.2005.31

    MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    Çinar C: On the difference equation xn+1 = x n -1 /-1+ x n x n -1 . Applied Mathematics and Computation 2004,158(3):813–816. 10.1016/j.amc.2003.08.122

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    Çinar C: On the positive solutions of the difference equation x n +1 = ax n -1 /1+ bx n x n -1 . Applied Mathematics and Computation 2004,156(2):587–590. 10.1016/j.amc.2003.08.010

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Çinar C: On the positive solutions of the difference equation x n +1 = x n -1 /1+ x n x n -1 . Applied Mathematics and Computation 2004,150(1):21–24. 10.1016/S0096-3003(03)00194-2

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Elabbasy EM, El-Metwally H, Elsayed EM: On the periodic nature of some max-type difference equations. International Journal of Mathematics and Mathematical Sciences 2005,2005(14):2227–2239. 10.1155/IJMMS.2005.2227

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Elabbasy EM, El-Metwally H, Elsayed EM: On the Difference Equation . to appear in Journal of Concrete and Applicable Mathematics

  7. 7.

    El-Metwally H, Grove EA, Ladas G: A global convergence result with applications to periodic solutions. Journal of Mathematical Analysis and Applications 2000,245(1):161–170. 10.1006/jmaa.2000.6747

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    El-Metwally H, Grove EA, Ladas G, Voulov HD: On the global attractivity and the periodic character of some difference equations. Journal of Difference Equations and Applications 2001,7(6):837–850. 10.1080/10236190108808306

    MathSciNet  Article  MATH  Google Scholar 

  9. 9.

    Kocić VL, Ladas G: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Mathematics and Its Applications. Volume 256. Kluwer Academic, Dordrecht; 1993:xii+228.

    Google Scholar 

  10. 10.

    Kulenovic MRS, Ladas G: Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures. Chapman & Hall/CRC, Florida; 2001.

    Google Scholar 

  11. 11.

    Migda M, Musielak A, Schmeidel E: On a class of fourth-order nonlinear difference equations. Advances in Difference Equations 2004,2004(1):23–36. 10.1155/S1687183904308083

    MathSciNet  Article  MATH  Google Scholar 

  12. 12.

    Philos ChG, Purnaras IK: An asymptotic result for some delay difference equations with continuous variable. Advances in Difference Equations 2004,2004(1):1–10. 10.1155/S1687183904310058

    MathSciNet  Article  MATH  Google Scholar 

  13. 13.

    Sun T, Xi H, Hong L: On the system of rational difference equations x n +1 = f ( x n , yn-k), y n +1 = f ( y n , xn-k). Advances in Difference Equations 2006, 2006: 7 pages.

    MathSciNet  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to EM Elabbasy.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Elabbasy, E., El-Metwally, H. & Elsayed, E. On the Difference equation xn+ = ax n - bx n /(cx x - dxn-1). Adv Differ Equ 2006, 082579 (2006). https://doi.org/10.1155/ADE/2006/82579

Download citation

Keywords

  • Differential Equation
  • Real Number
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis