@article{article_474649, title={Solvability of a system of higher order nonlinear difference equations}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={49}, pages={1566–1593}, year={2020}, DOI={10.15672/hujms.474649}, author={Kara, Merve and Yazlik, Yasin and Tollu, Durhasan Turgut}, keywords={System of difference equations, Asymptotic behavior, Fibonacci sequence, Forbidden set}, abstract={<p>In this paper we show that the system of difference equations </p> <p>\[ x_n= a y_{n-k}+\frac{dy_{n-k}x_{n-( k+l ) }{b x_{n-(k+l)}+cy_{n-l }=\alpha x_{n-k}+\frac{\delta x_{n-k}y_{n-(k+l) }{\beta y_{n-(k+l) }+\gamma x_{n-l}, \]   </p> <p> </p> <p> <span style="font-size:12px;">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. </span> </p>}, number={5}, publisher={Hacettepe University}