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http://dx.doi.org/10.4134/CKMS.c180472

A SOLVABLE SYSTEM OF DIFFERENCE EQUATIONS  

Taskara, Necati (Department of Mathematics Selcuk University)
Tollu, Durhasan T. (Department of Mathematics-Computer Science Necmettin Erbakan University)
Touafek, Nouressadat (LMAM Laboratory, Department of Mathematics Mohamed Seddik Ben Yahia University)
Yazlik, Yasin (Department of Mathematics Nevsehir Haci Bektas Veli University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.1, 2020 , pp. 301-319 More about this Journal
Abstract
In this paper, we show that the system of difference equations $x_n={\frac{ay^p_{n-1}+b(x_{n-2}y_{n-1})^{p-1}}{cy_{n-1}+dx^{p-1}_{n-2}}}$, $y_n={\frac{{\alpha}x^p_{n-1}+{\beta}(y_{n-2}x_{n-1})^{p-1}}{{\gamma}x_{n-1}+{\delta}y^{p-1}_{n-2}}}$, n ∈ ℕ0 where the parameters a, b, c, d, α, β, γ, δ, p and the initial values x-2, x-1, y-2, y-1 are real numbers, can be solved. Also, by using obtained formulas, we study the asymptotic behaviour of well-defined solutions of aforementioned system and describe the forbidden set of the initial values. Our obtained results significantly extend and develop some recent results in the literature.
Keywords
Difference equations; solution in closed-form; forbidden set; asymptotic behaviour;
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