Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2018.11.15
  • Accepted : 2019.07.17
  • Published : 2020.01.31
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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.

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References

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