Solutions of the Rational Difference Equations

Year 2018, Volume: 6 Issue: 2, 177 - 192, 24.12.2018

Dagıstan Şimşek Peil Esengul Kyzy

https://izlik.org/JA33PX54FC

Abstract

In
this paper the solutions of the following difference equation is examined,

(1)

where
the initial conditions are positive real numbers.

Keywords

Difference equation

References

• [1] Amleh A. M., Grove E. A., Ladas G., Georgiou D. A., On the recursive sequence , J. Math. Anal. Appl., 233, no. 2, (1999),790-798.
• [2] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 158 (3), (2004), 809–812.
• [3] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 158 (3), (2004), 793–797.
• [4] Cinar C., On the positive solutions of the difference equation, Appl. Math. Comp., 156 (3), (2004), 587–590.
• [5] Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation , Advances in Difference Equation, (2006), 1-10.
• [6] Elabbasy E. M., El-Metwally H., Elsayed E. M., Qualitative behavior of higher order difference equation, Soochow Journal of Mathematics, 33(4), (2007), 861-873.
• [7] Elabbasy E. M., El-Metwally H., Elsayed E. M., Global attractivity and periodic character of a fractional difference equation of order three, Yokohama Mathematical Journal, 53, (2007), 89-100.
• [8] Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation , J. Conc. Appl. Math., 5(2), (2007), 101-113.
• [9] Elabbasy E. M. and Elsayed E. M., On the Global Attractivity of Difference Equation of Higher Order, Carpathian Journal of Mathematics, 24 (2), (2008), 45–53.
• [10] Elsayed E. M., On the Solution of Recursive Sequence of Order Two, Fasciculi Mathematici, 40, (2008), 5–13.
• [11] Elsayed E. M., Dynamics of a Recursive Sequence of Higher Order, Communications on Applied Nonlinear Analysis, 16 (2), (2009), 37–50.
• [12] Elsayed E. M., Solution and atractivity for a rational recursive sequence, Discrete Dynamics in Nature and Society, (2011), 17.
• [13] Elsayed E. M., On the solution of some difference equation, Europan Journal of Pure and Applied Mathematics, 4 (3), (2011), 287–303.
• [14] Elsayed E. M., On the Dynamics of a higher order rational recursive sequence, Communications in Mathematical Analysis, 12 (1), (2012), 117–133.
• [15] Elsayed E. M., Solution of rational difference system of order two, Mathematical and Computer Modelling, 55, (2012), 378–384.
• [16] Gibbons C. H., Kulenović M. R. S. and Ladas G., On the recursive sequence , Math. Sci. Res. Hot-Line, 4, 2, (2000), 1-11.
• [17] Kulenović M.R.S., Ladas G., Sizer W.S., On the recursive sequence Math. Sci. Res. Hot-Line, 2, 5, (1998), 1-16.
• [18] Stevic S., On the recursive sequence , Taiwanese J. Math., 6, 3, (2002), 405-414.
• [19] Şimşek D., Çınar C. and Yalçınkaya İ., On the recursive sequence , Int. J. Contemp. Math. Sci., 1, 9-12, (2006), 475-480.
• [20] Şimşek D., Çınar C., Karataş R., Yalçınkaya İ., On the recursive sequence , Int. J. Pure Appl. Math., 27, 4, (2006), 501-507.
• [21] Şimşek D., Çınar C., Karataş R., Yalçınkaya İ., "n the recursive sequence , Int. J. Pure Appl. Math., 28, 1, (2006), 117-124.
• [22] Şimşek D., Çınar C., Yalçınkaya İ., On The Recursive Sequence x(n+1) = x[n-(5k+9)] / 1+x(n-4)x(n-9) x[n-(5k+4)], Taiwanese Journal of Mathematics, Vol. 12, 5, (2008), 1087-1098.
• [23] Şimşek D., Doğan A., On A Class of Recursive Sequence, Manas Journal of Engineering, 2, 1, (2014), 16-22.
• [24] Şimşek D., Eröz M., Solutions of The Rational Difference Equations , Manas Journal of Engineering, 4, 1, (2016), 12-20.