6533b836fe1ef96bd12a0760

RESEARCH PRODUCT

On the Second Order Rational Difference Equation $$x_{n+1}=\beta +\frac{1}{x_n x_{n-1}}$$ x n + 1 = β + 1 x n x n - 1

Aija Anisimova

subject

CombinatoricsCharacter (mathematics)ConjectureRational difference equationOpen problemMathematical analysisOrder (ring theory)Beta (velocity)Mathematics

description

The author investigates the local and global stability character, the periodic nature, and the boundedness of solutions of the second-order rational difference equation $$x_{n+1}=\beta +\frac{1}{x_{n}x_{n-1}}, \quad n=0,1,\ldots ,$$ with parameter \(\beta \) and with arbitrary initial conditions such that the denominator is always positive. The main goal of the paper is to confirm Conjecture 8.1 and to solve Open Problem 8.2 stated by A.M. Amleh, E. Camouzis and G. Ladas in On the Dynamics of a Rational Difference Equations I (International Journal of Difference Equations, Volume 3, Number 1, 2008, pp.1–35).

yearjournalcountryeditionlanguage
2016-01-01
https://doi.org/10.1007/978-3-662-52927-0_1