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1. On a Conjecture for a Higher-Order Rational Difference Equation.

Author

Maoxin Liao, Xianhua Tang, and Changjin Xu

Subjects
*DIFFERENTIAL equations, *ASYMPTOTIC theory of algebraic ideals, *DIFFERENCE equations, *ASYMPTOTIC expansions, *SIGNED numbers, *DIFFERENTIAL-difference equations
Abstract

This paper studies the global asymptotic stability for positive solutions to the higher order rational difference equation xn = Π mj=1(xn-kj + 1) + Π mj=1(xn-kj - 1))/(Π mj=1(xn-kj + 1) - Π mj=1(xn-kj - 1)) n = 0, 1, 2, . . ., where m is odd and x-km, x-km+1, . . . , x-1 ∈. (0, ∞). Our main result generalizes several others in the recent literature and confirms a conjecture by Berenhaut et al., 2007. [ABSTRACT FROM AUTHOR]

Published
2009
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