Global behavior of certain nonautonomous linearizable three term difference equations (Q6156685)

Summary: We investigate the nonautonomous difference equation with real initial conditions and coefficients \(g_i, i = 0, 1\) which are in general functions of \(n\) and/or the state variables \(x_n, x_{n - 1}, \ldots \), and satisfy \(g_0 + g_1 = 1\). We also obtain some global results about the behavior of solutions of the nonautonomous non-homogeneous difference equation where \(g_i, i = 0, 1, 2\) are functions of \(n\) and/or the state variables \(x_n, x_{n - 1}, \ldots \), with \(g_0 + g_1 = 1\). Our results are based on the explicit formulas for solutions. We illustrate our results by numerous examples.