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We investigate the nonautonomous difference equation with real initial conditions and coefficients gi,i=0,1gii01which are in general functions of n and/or the state variables xn,xn−1,…xnxn1 , and satisfy g0+g1=1g0g11 . We also obtain some global results about the behavior of solutions of the nonautonomous non-homogeneous difference equation where gi,i=0,1,2gii012 are functions of n and/or the state variables xn,xn−1,…xnxn1 , with g0+g1=1g0g11 . 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
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