6533b827fe1ef96bd12859a3

RESEARCH PRODUCT

Periodic Solutions of the Second Order Quadratic Rational Difference Equation $$x_{n+1}=\frac{\alpha }{(1+x_n)x_{n-1}} $$ x n + 1 = α ( 1 + x n ) x n - 1

Inese Bula

subject

CombinatoricsEquilibrium pointQuadratic equationRational difference equationPeriod (periodic table)Differential equationOpen problemMathematical analysisOrder (ring theory)Prime (order theory)Mathematics

description

The aim of this article is to investigate the periodic nature of solutions of a rational difference equation $$x_{n+1}=\frac{\alpha }{(1+x_n)x_{n-1}}. {(*)} $$ We explore Open Problem 3.3 given in Amleh et al. (Int J Differ Equ 3(1):1–35, 2008, [2]) that requires to determine all periodic solutions of the equation (*). We conclude that for the equation (*) there are no periodic solution with prime period 3 and 4. Period 7 is first period for which exists nonnegative parameter \(\alpha \) and nonnegative initial conditions.

yearjournalcountryeditionlanguage
2016-01-01
https://doi.org/10.1007/978-3-662-52927-0_3