Electron. J. Diff. Equ., Vol. 2015 (2015), No. 308, pp. 1-14.

First-order product-type systems of difference equations solvable in closed form

Stevo Stevic

Abstract:
We show that the first-order system of difference equations
$$ z_{n+1}=\alpha z_n^aw_n^b,\quad w_{n+1}=\beta z_n^cw_n^d,\quad n\in\mathbb{N}_0, $$
where $a,b,c,d\in\mathbb{Z}$, $\alpha,\beta \in\mathbb{C}\setminus\{0\}$, $z_0, w_0\in\mathbb{C}\setminus\{0\}$, is solvable in closed form, by finding closed form formulas of its solutions.

Submitted August 29, 2015. Published December 21, 2015.
Math Subject Classifications: 39A20, 39A45.
Key Words: Difference equation; first order system;product-type system; solvable in closed form.

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Stevo Stevic
Mathematical Institute of the Serbian Academy of Sciences
Knez Mihailova 36/III, 11000 Beograd, Serbia
email: sstevic@ptt.rs

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