Global Behavior of Certain Nonautonomous Linearizable Three Term Difference Equations

E. J. Janowski and M. R. S. Kulenović
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E. J. Janowski: Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA
M. R. S. Kulenović: Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA

Mathematics, 2018, vol. 6, issue 5, 1-19

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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