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An explicit formula and forbidden set for a higher order difference equation

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Abstract

In this paper, we determine the forbidden set, introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation

$$\begin{aligned} x_{n+1}=\frac{ax_{n}x_{n-k+1}}{ bx_{n-k+1}+ cx_{n-k}},\quad n=0,1,\ldots , \end{aligned}$$

where a, b, c are positive real numbers, the initial conditions \( x_{-k}, x_{-k+1},\ldots ,x_{-1},x_0\) are real numbers and k is a positive integer.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey

    M. Gümüş

  2. Department of Basic Science, The Valley Higher Institute of Engineering and Technology, Cairo, Egypt

    R. Abo-Zeid

Authors
  1. M. Gümüş
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  2. R. Abo-Zeid
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Correspondence to M. Gümüş.

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Gümüş, M., Abo-Zeid, R. An explicit formula and forbidden set for a higher order difference equation. J. Appl. Math. Comput. 63, 133–142 (2020). https://doi.org/10.1007/s12190-019-01311-9

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