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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.

##### MSC:
 39A11 Stability of difference equations (MSC2000) 39A20 Multiplicative and other generalized difference equations
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##### References:
 [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
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