Global Behavior of Certain Nonautonomous Linearizable Three Term Difference Equations

We investigate the nonautonomous difference equation with real initial conditions and coefficients gi,i=0,1gi,i=0,1 which are in general functions of n and/or the state variables xn,xn−1,…xn,xn−1,… , and satisfy g0+g1=1g0+g1=1 . We also obtain some global results about the behavior of solutions of the nonautonomous non-homogeneous difference equation where gi,i=0,1,2gi,i=0,1,2 are functions of n and/or the state variables xn,xn−1,…xn,xn−1,… , with g0+g1=1g0+g1=1 . Our results are based on the explicit formulas for solutions. We illustrate our results by numerous examples.