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On a solvable system of p difference equations of higher order

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Abstract

In this paper we present the well-defined solution of the following system of higher-order rational difference equations:

$$\begin{aligned} x^{(j)}_{n+1}=\frac{x^{(j+1)\pmod {p}}_{n-k}}{a+bx^{(j+1)\pmod {p}}_{n-k}},\quad n, p, k\in \mathbb {N}_0 , j=\overline{1,p}, \end{aligned}$$

where the parameters a, b are nonzero real numbers and the initial values \(x^{(j)}_{-k}\), \(x^{(j)}_{-k+1}\),\(\ldots \), \(x^{(j)}_{-1}\) and \(x^{(j)}_0,\) \(j=\overline{1,p}\), do not equal \(-\frac{a}{b}\). Some theoretical explanations related to the representation for the general solution are also given.

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Acknowledgements

The authors Y. Halim, A. Khelifa and A. Bouchair were supported by DGRSDT, Algeria.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Abdelhafid Boussouf University Center, RP 26, 43000, Mila, Mila, Algeria

    Yacine Halim

  2. LMAM Laboratory, Mohamed Seddik Ben Yahia University, BP 98, 18000, Ouled Aissa, Jijel, Algeria

    Amira Khelifa & Abderrahmane Bouchair

  3. Department of Applied Mathematics, University of Alicante, Carretera Sant Vicent del Raspeig, Alicante, Spain

    Messaoud Berkal

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  1. Yacine Halim
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  2. Amira Khelifa
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  4. Abderrahmane Bouchair
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Correspondence to Yacine Halim.

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Halim, Y., Khelifa, A., Berkal, M. et al. On a solvable system of p difference equations of higher order. Period Math Hung 85, 109–127 (2022). https://doi.org/10.1007/s10998-021-00421-x

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