Solutions of the Rational Difference Equations

Yıl 2018, Cilt: 6 Sayı: 2, 177 - 192, 24.12.2018

Dagıstan Şimşek Peil Esengul Kyzy

Öz

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

(1)

where
the initial conditions are positive real numbers.

Anahtar Kelimeler

Difference equation

Kaynakça

• [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.