Opuscula Math. 26, no. 3 (2006), 387-394

Opuscula Mathematica

# Further properties of the rational recursive sequence x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}

Anna Andruch-Sobiło
Małgorzata Migda

Abstract. In this paper we consider the difference equation $x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}, \quad n=0,1,...\tag{E}$ with positive parameters $$a$$ and $$c$$, negative parameter $$b$$ and nonnegative initial conditions. We investigate the asymptotic behavior of solutions of equation $$\text{(E)}$$.

Keywords: difference equation, explicit formula, positive solutions, asymptotic stability.

Mathematics Subject Classification: 39A10.

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