On a k-Order System of Lyness-Type Difference Equations

Abstract

(ai−1xi−1(n) + bi−1)/xi−2(n − 1), i = 3,4,...,k, where ai, bi, i = 1,2,...,k, are positive con-stants, k ≥ 3 is an integer, and the initial values are positive real numbers. We study the existence of invariants, the boundedness, the persistence, and the periodicity of the posi-tive solutions of this system. Copyright © 2007 G. Papaschinopoulos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, dis-tribution, and reproduction in any medium, provided the original work is properly cited. 1.