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ON A SOLVABLE DIFFERENCE EQUATION WITH SEQUENCE COEFFICIENTS
Keywords:
difference equation, solution, equilibrium point, asymptotic behavior.DOI:
https://doi.org/10.17654/0974165822017Abstract
This paper shows the asymptotic behavior of solutions of the difference equation
$$
x_{n+1}=\frac{a_n x_{n-2 k}}{b_n+c_n \prod_{i=0}^{2 k} x_{n-i}},
$$
where $a_n, b_n$ and $c_n$ are sequences of positive real numbers and initial conditions are nonzero real numbers.
Received: January 5, 2022
Accepted: February 23, 2022
References
R. Abo-Zeid, Behavior of solutions of higher order difference equation, Alabama Journal of Mathematics 42 (2018), 1-10.
M. B. Almatrafi, E. M. Elsayed and F. Alzahrani, Investigating some properties of a fourth order difference equation, J. Comput. Anal. Appl. 28(2) (2020), 243-253.
M. Ari and A. Gelisken, Periodic and asymptotic behavior of a difference equation, Asian-Eur. J. Math. 12(6) (2019), 2040004, 10 pp.
G. Cinar, A. Gelisken and O. Ozkan, Well-defined solutions of the difference equation $x_n=frac{x_{n-3 k} x_{n-4 k} x_{n-5 k}}{x_{n-k} x_{n-2 k}left( pm 1 pm x_{n-3 k} x_{n-4 k} x_{n-5 k}right)}$, Asian-Eur. J. Math. $12(6)(2019), 2040016,13, mathrm{pp}$
E. M. Elsayed, F. Alzahrani and H. S. Alayachi, Formulas and properties of some class of nonlinear difference equation, J. Comput Anal Appl. 24(8) (2018), $1517-1531$
S. Ergin and R. Karatas, $mathrm{On}$ the solutions of the recursive sequence $x_{n+1}=frac{a x_{n-k}}{a-prod_{i=0}^k x_{n-i}}$, Thai J. Math. 14(2) (2016), 391-397.
R. Karatas, Global behavior of a higher order difference equation, Comput Math. Appl. 60 (2010), 830-839.
R. Karatas, On the solutions of the recursive sequence $x_{n+1}=$ $frac{alpha x_{n-(2 k+1)}}{-a+x_{n-k} x_{n-(2 k+1)}}$, Fasc. Math. $45(2010), 37-45$.
R. Karatas and A. Gelisken, A solution form of a higher order difference equation, Konuralp J. Math. $9(2)(2021), 316-323$.
A. S. Kurbani, C. Cinar and I. Yalcinkaya, On the behavior of positive solutions of the system of rational difference equations $x_{n+1}=frac{x_{n-1}}{y_n x_{n-1}+1}, quad y_{n+1}=$ $frac{y_{n-1}}{x_n y_{n-1}+1}$, Math. Comput Modelling 53 (2011), 1261-1267.
O. Ozkan and A. S. Kurbanli, On a system of difference equations, Discrete Dyn. Nat Soc 2013 Att, ID $970316,7 mathrm{pp}$.
D. Simsek and F. Abdullayev, On the recursive sequence $x_{n+1}=$ $frac{x_{n-(4 k+3)}}{1+prod_{t=0}^2 x_{n-(k+1) t-k}}$, J. Math. Sci. (N.Y.) 222(6) (2017), 762-771.
D. Simsek and F. Abdullayev, On the recursive sequence $x_{n+1}=$ $frac{x_{n-(k+1)}}{1+x_n x_{n-1} cdots x_{n-k}}$, J. Math. Sci. (N.Y.) $234(1)$ (2018), 73-81
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