ON THE NATURE OF SOLUTIONS OF THE DIFFERENCE EQUATION X<sub>N+1</sub> = X<sub>N</sub>X<sub>N-3</sub> - 1

Author(s):

C. M. Kent , W. Kosmala

Abstract:

We investigate the long-term behavior of solutions of the di erence equation xn+1 = xnxn-3 - 1; n = 0; 1; :: :; where the initial conditions x-3; x-2; x-1; x0 are real numbers. In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

Keywords:

Difference Equations , Boundedness , Periodicity , Asymptotic periodicity , Eventual periodicity , Invariant interval , Continued fractions

Language:
English
Published:
International Journal Of Nonlinear Analysis And Applications, Volume:2 Issue: 2, Winter - Spring 2011
Pages:
24 to 43
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