zbMATH — the first resource for mathematics

Boundedness of positive solutions of second-order rational difference equations. (English) Zbl 1064.39006
The authors study the positive solutions for the rational difference equations with nonnegative coefficients of the form \( x_{n+1}=\frac{\alpha +\beta x_n+\gamma x_{n-1}}{A+Bx_n+Cx_{n-1}}. \) They provide necessary and sufficient conditions of the coefficients parameters in order for the positive solutions to be bounded, and deal with three conjectures and one open problem.

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
Full Text: DOI
[1] Gibbons CH, New Trends in Difference Equations, Taylor & Francis pp 141– (2002)
[2] Gibbons CH, Math. Sci. Res. Hot-Line 4 pp 1– (2000)
[3] DOI: 10.1006/jmaa.2000.7032 · Zbl 0967.39004
[4] DOI: 10.1201/9781420035384
[5] DOI: 10.1016/S0898-1221(03)00090-7 · Zbl 1077.39004
[6] DOI: 10.1006/jmaa.2000.7032 · Zbl 0967.39004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.