TY  - JOUR
T1  - Solvability of a system of higher order nonlinear difference equations
AU  - Yazlik, Yasin
AU  - Kara, Merve
AU  - Tollu, Durhasan Turgut
PY  - 2020
DA  - October
DO  - 10.15672/hujms.474649
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1566
EP  - 1593
VL  - 49
IS  - 5
LA  - en
AB  - In this paper we show that the system of difference equations\[ x_n= a y_{n-k}+\frac{dy_{n-k}x_{n-( k+l ) }}{b x_{n-(k+l)}+cy_{n-l}}=\alpha x_{n-k}+\frac{\delta x_{n-k}y_{n-(k+l)}}{\beta y_{n-(k+l)}}+\gamma x_{n-l}, \] where $n\in \mathbb{N}_{0},$ $k$ and $l$ are positive integers, the parameters $a$, $b$, $c$, $d$, $\alpha $, $\beta $, $\gamma $, $\delta $ are real numbers and the initial values $x_{-j}$, $y_{-j}$, $j=\overline{1,k+l}$, are real numbers, can be solved in the closed form. We also determine the asymptotic behavior of solutions for the case $l=1$ and describe the forbidden set of the initial values using the obtained formulas. Our obtained results significantly extend and develop some recent results in the literature.
KW  - System of difference equations
KW  - Asymptotic behavior
KW  - Fibonacci sequence
KW  - Forbidden set
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UR  - https://doi.org/10.15672/hujms.474649
L1  - https://dergipark.org.tr/en/download/article-file/970408
ER  -