In this paper we show that the system of difference equations
\[ x_n= a y_{nk}+\frac{dy_{nk}x_{n( k+l ) }}{b x_{n(k+l)}+cy_{nl}}=\alpha x_{nk}+\frac{\delta x_{nk}y_{n(k+l)}}{\beta y_{n(k+l)}}+\gamma x_{nl}, \]
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.
Primary Language  en 

Subjects  Mathematics 
Journal Section  Mathematics 
Authors 

Dates 
Publication Date : October 6, 2020 
Bibtex  @research article { hujms474649,
journal = {Hacettepe Journal of Mathematics and Statistics},
issn = {2651477X},
eissn = {2651477X},
address = {},
publisher = {Hacettepe University},
year = {2020},
volume = {49},
pages = {1566  1593},
doi = {10.15672/hujms.474649},
title = {Solvability of a system of higher order nonlinear difference equations},
key = {cite},
author = {Kara, Merve and Yazli̇k, Yasin and Tollu, Durhasan Turgut}
} 
APA  Kara, M , Yazli̇k, Y , Tollu, D . (2020). Solvability of a system of higher order nonlinear difference equations . Hacettepe Journal of Mathematics and Statistics , 49 (5) , 15661593 . DOI: 10.15672/hujms.474649 
MLA  Kara, M , Yazli̇k, Y , Tollu, D . "Solvability of a system of higher order nonlinear difference equations" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 15661593 <https://dergipark.org.tr/en/pub/hujms/issue/57199/474649> 
Chicago  Kara, M , Yazli̇k, Y , Tollu, D . "Solvability of a system of higher order nonlinear difference equations". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 15661593 
RIS  TY  JOUR T1  Solvability of a system of higher order nonlinear difference equations AU  Merve Kara , Yasin Yazli̇k , Durhasan Turgut Tollu Y1  2020 PY  2020 N1  doi: 10.15672/hujms.474649 DO  10.15672/hujms.474649 T2  Hacettepe Journal of Mathematics and Statistics JF  Journal JO  JOR SP  1566 EP  1593 VL  49 IS  5 SN  2651477X2651477X M3  doi: 10.15672/hujms.474649 UR  https://doi.org/10.15672/hujms.474649 Y2  2019 ER  
EndNote  %0 Hacettepe Journal of Mathematics and Statistics Solvability of a system of higher order nonlinear difference equations %A Merve Kara , Yasin Yazli̇k , Durhasan Turgut Tollu %T Solvability of a system of higher order nonlinear difference equations %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651477X2651477X %V 49 %N 5 %R doi: 10.15672/hujms.474649 %U 10.15672/hujms.474649 
ISNAD  Kara, Merve , Yazli̇k, Yasin , Tollu, Durhasan Turgut . "Solvability of a system of higher order nonlinear difference equations". Hacettepe Journal of Mathematics and Statistics 49 / 5 (October 2020): 15661593 . https://doi.org/10.15672/hujms.474649 
AMA  Kara M , Yazli̇k Y , Tollu D . Solvability of a system of higher order nonlinear difference equations. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 15661593. 
Vancouver  Kara M , Yazli̇k Y , Tollu D . Solvability of a system of higher order nonlinear difference equations. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 15661593. 