Global Behavior of Certain Nonautonomous Linearizable Three Term Difference Equations

Abstract

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 , … , 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 , … , with g 0 + g 1 = 1 . Our results are based on the explicit formulas for solutions. We illustrate our results by numerous examples.

Keywords

• difference equation
• identity
• linear
• nonautonomous
• periodic
• stability
• solution