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Global Behavior of Certain Nonautonomous Linearizable Three Term Difference Equations

Author

Listed:
  • 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)

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.

Suggested Citation

  • E. J. Janowski & M. R. S. Kulenović, 2018. "Global Behavior of Certain Nonautonomous Linearizable Three Term Difference Equations," Mathematics, MDPI, vol. 6(5), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:5:p:79-:d:145470
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    References listed on IDEAS

    as
    1. A. Bilgin & M. R. S. Kulenović, 2017. "Global Asymptotic Stability for Discrete Single Species Population Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-15, June.
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