Global Behavior of Certain Nonautonomous Linearizable Three Term Difference Equations

• Main Authors: E. J. Janowski, M. R. S. Kulenović
• Format: Article
• Language: English
• Published: MDPI AG 2018-05-01
• Series: Mathematics
• Subjects: difference equation; identity; linear; nonautonomous; periodic; stability; solution
• Online Access: http://www.mdpi.com/2227-7390/6/5/79

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.