On the solutions of a second order difference equation
Mathematica Moravica, Tome 21 (2017) no. 2.

Voir la notice de l'article dans eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this paper, we discuss the global behavior of all solutions of the difference equation $x_{n+1} = \frac{x_{n}x_{n-1}}{ax_{n} + bx_{n-1}},\quad n\in\mathbb{N}_{0},$ where $a,b$ are real numbers and the initial conditions $x_{-1},x_{0}$ are real numbers. We determine the forbidden set and give an explicit formula for the solutions. We show the existence of periodic solutions, under certain conditions.
Mots-clés : difference equation, forbidden set, periodic solution, unbounded solution 
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R. Abo-Zeid. On the solutions of a second order difference equation. Mathematica Moravica, Tome 21 (2017) no. 2. https://geodesic-test.mathdoc.fr/item/MM3_2017_21_2_a4/