Turkish Journal of Mathematics
Abstract
In this paper, we show that the following higher-order system of nonlinear difference equations, $ x_{n}=\frac{x_{n-k}y_{n-k-l}}{y_{n-l}\left( a_{n}+b_{n}x_{n-k}y_{n-k-l}\right)}, \ y_{n}=\frac{y_{n-k}x_{n-k-l}}{x_{n-l}\left( \alpha_{n}+\beta_{n}y_{n-k}x_{n-k-l}\right)}, \ n\in \mathbb{N}_{0}, $ where $k,l\in \mathbb{N}$, $\left(a_{n} \right)_{n\in \mathbb{N}_{0}}, \left(b_{n} \right)_{n\in \mathbb{N}_{0}}, \left(\alpha_{n} \right)_{n\in \mathbb{N}_{0}}, \left(\beta_{n} \right)_{n\in \mathbb{N}_{0}}$ and the initial values $x_{-i}, \ y_{-i}$, $i=\overline {1,k+l}$, are real numbers, can be solved and some results in the literature can be extended further. Also, by using these obtained formulas, we investigate the asymptotic behavior of well-defined solutions of the above difference equations system for the case $k=2, l=k$.
DOI
10.3906/mat-1902-24
Keywords
System of nonlinear difference equations, solution of system of difference equations in closed form, asymptotic behavior
First Page
1533
Last Page
1565
Recommended Citation
KARA, MERVE and YAZLIK, YASİN
(2019)
"Solvability of a system of nonlinear difference equations of higher order,"
Turkish Journal of Mathematics: Vol. 43:
No.
3, Article 54.
https://doi.org/10.3906/mat-1902-24
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss3/54
