The nature of solutions of the difference equation x_{n} = max{A/x_{n2},B/x_{n3}^{α}}
Abstract
We consider positive solutions of the difference equation x_{n} = max{A/x_{n2},B/xn3α},n≥0, where A ≥ 0, B ≥ 0, 0 < α ≤ 1 and the initial conditions x_{1} x_{2}, x_{3} are arbitrary positive real numbers. We show that every positive solution of this difference equation approaches x¯ = √B or is eventually periodic with period 4, 5 or 6. Also, this work confirms partially the conjecture proposed in [18].
 Publication:

First International Conference on Analysis and Applied Mathematics: ICAAM 2012
 Pub Date:
 August 2012
 DOI:
 10.1063/1.4747636
 Bibcode:
 2012AIPC.1470...50G
 Keywords:

 difference equations;
 02.30.f;
 Function theory analysis