Also, by using these obtained formulas,we investigate the asymptotic behavior of well-defined solutions of the above difference equations system for the casek = 2; l = k .
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we show that the following higher-order system of nonlinear difference equations, $x_{n=}frac{x_{n-kYn-k-l}}{Yn-l(a_n+b_nx_n-kYn-k-l)}$, $Y_{n=}frac{Y_{n-kxn-k-l}}{xn-l(a_n+b_nY_n-kxn-k-l)}$, $nin{mathbb{N}}_0$where k; l 2 N, (an)n2N0; (bn)n2N0; (n)n2N0; (n)n2N0and the initial values xi; yi , i = 1; k + l , are real numbers,can be solved and some results in the literature can be extended further.
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Key Findings & Data:In this paper, we show that the following higher-order system of nonlinear difference equations, $x_{n=}frac{x_{n-kYn-k-l}}{Yn-l(a_n+b_nx_n-kYn-k-l)}$, $Y_{n=}frac{Y_{n-kxn-k-l}}{xn-l(a_n+b_nY_n-kxn-k-l)}$, $nin{mathbb{N}}_0$where k; l 2 N, (an)n2N0; (bn)n2N0; (n)n2N0; (n)n2N0and the initial values xi; yi , i = 1; k + l , are real numbers,can be solved and some results in the literature can be extended further.
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Conclusion & Impact:Also, by using these obtained formulas,we investigate the asymptotic behavior of well-defined solutions of the above difference equations system for the casek = 2; l = k .
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, we show that the following higher-order system of nonlinear difference equations, $x_{n=}frac{x_{n-kYn-k-l}}{Yn-l(a_n+b_nx_n-kYn-k-l)}$, $Y_{n=}frac{Y_{n-kxn-k-l}}{xn-l(a_n+b_nY_n-kxn-k-l)}$, $nin{mathbb{N}}_0$where k; l 2 N, (an)n2N0; (bn)n2N0; (n)n2N0; (n)n2N0and the initial values xi; yi , i = 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 casek = 2; l = k .
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Cite This Article
KARA, M., YAZLIK, Y. (2022). Solvability of a system of nonlinear difference equations of higher order. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 3, 1533–1565. https://ajindex.com/articles/608027
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