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Zbl 1064.39006
Huang, Y.S.; Knopf, P.M.
Boundedness of positive solutions of second-order rational difference equations.
(English)
[J] J. Difference Equ. Appl. 10, No. 11, 935-940 (2004). ISSN 1023-6198

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.
[Wan-Tong Li (Lanzhou)]
MSC 2000:
*39A11 Stability of difference equations
39A20 Generalized difference equations

Keywords: positive solutions; bounded solution; coefficient parameters; nonnegative coefficients

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