Opuscula Mathematica

Opuscula Math.
, no. 3
 (), 387-394
Opuscula Mathematica

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

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.
Cite this article as:
Anna Andruch-Sobiło, Małgorzata Migda, Further properties of the rational recursive sequence x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}, Opuscula Math. 26, no. 3 (2006), 387-394
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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