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We investigate the nonautonomous difference equation with real initial conditions and coefficients gi, i = 0,1 which are in general functions of n and/or the state variables xn, xn−1,…xnxn1 , and satisfy g0+g1 = 1. We also obtain some global results about the behavior of solutions of the nonautonomous non-homogeneous difference equation where gi, i = 0, 1, 2 are functions of n and/or the state variables xn, xn−1,…, with g0 + g1 = 1. Our results are based on the explicit formulas for solutions. We illustrate our results by numerous examples.
Janowski, E.J.; Kulenović, M.R.S. Global Behavior of Certain Nonautonomous Linearizable Three Term Difference Equations. Mathematics 2018, 6, 79. https://doi.org/10.3390/math6050079
Available at: https://doi.org/10.3390/math6050079
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