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A note on unbounded solutions of a class of second order rational difference equations. (English) Zbl 1107.39007
The authors study the difference equation \[ x_{n+1}=\frac{\alpha+\beta x_n +\gamma x_{n-1}}{A+B x_n +C x_{n-1}}, \] where all coefficients and initial conditions are nonnegative, \(A+B x_n +C x_{n-1}>0\) for all \(n\). A characterization of unbounded solutions for this equation is presented.
The paper aswers two open problems posed by M. R. S. Kulenović and G. Ladas [Dynamics of second order rational difference equations. With open problems and conjectures, London: Chapman and Hall/CRC (2001; Zbl 0981.39011)]

MSC:
39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
Keywords:
stable manifold
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References:
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