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## Solvability of a system of higher order nonlinear difference equations

#### Merve KARA [1] , Yasin YAZLİK [2] , Durhasan Turgut TOLLU [3]

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.

System of difference equations, Asymptotic behavior, Fibonacci sequence, Forbidden set
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Primary Language en Mathematics Mathematics Orcid: 0000-0001-8081-0254Author: Merve KARA Institution: AKSARAY UNIVERSITY, AKSARAY VOCATIONAL SCHOOLCountry: Turkey Orcid: 0000-0001-6369-540XAuthor: Yasin YAZLİK (Primary Author)Institution: NEVSEHIR HACI BEKTAS VELI UNIVERSITYCountry: Turkey Orcid: 0000-0002-3313-8829Author: Durhasan Turgut TOLLU Institution: Necmettin Erbakan UniversityCountry: Turkey Publication Date : October 6, 2020
 Bibtex @research article { hujms474649, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, 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) , 1566-1593 . 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 ): 1566-1593 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 ): 1566-1593 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 - 2651-477X-2651-477X 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 2651-477X-2651-477X %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): 1566-1593 . 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): 1566-1593. 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): 1566-1593.

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