Authors: | Stević, Stevo |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | On the recursive sequence xn + 1 = max {c, frac(xnp, xn - 1p)} |
Journal: | Applied Mathematics Letters |
Volume: | 21 |
Issue: | 8 |
First page: | 791 |
Last page: | 796 |
Issue Date: | 1-Aug-2008 |
Rank: | M22 |
ISSN: | 0893-9659 |
DOI: | 10.1016/j.aml.2007.08.008 |
Abstract: | This work studies the boundedness and global attractivity for the positive solutions of the difference equation xn + 1 = max {c, frac(underover(x, n, p), underover(x, n - 1, p))}, n ∈ N0, with p, c ∈ (0, ∞). It is shown that: (a) there exist unbounded solutions whenever p ≥ 4, (b) all positive solutions are bounded when p ∈ (0, 4), (c) every positive solution is eventually equal to 1 when p ∈ (0, 4) and c ≥ 1, (d) all positive solutions converge to 1 whenever p, c ∈ (0, 1). |
Keywords: | Boundedness | Difference equation | Global attractivity | Max type difference equations |
Publisher: | Elsevier |
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