Authors: | Stević, Stevo |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | Boundedness character of a class of difference equations |
Journal: | Nonlinear Analysis, Theory, Methods and Applications |
Volume: | 70 |
Issue: | 2 |
First page: | 839 |
Last page: | 848 |
Issue Date: | 15-Jan-2009 |
Rank: | M21a |
ISSN: | 0362-546X |
DOI: | 10.1016/j.na.2008.01.014 |
Abstract: | A complete picture regarding the boundedness character of positive solutions to the following difference equation xn = max {A, frac(underover(x, n - 1, p), underover(x, n - k, p))}, n ∈ N0, where k ≥ 2 and the parameters A and p are positive real numbers, is given. In particular, for the case pk - 1 ∈ (0, kk / (k - 1)k - 1), we prove that all solutions to the equation are bounded. We also present corresponding results concerning the following closely related difference equation xn = A + frac(xn - 1p, xn - kp), n ∈ N0 . |
Keywords: | Boundedness | Characteristic polynomial | Difference equation | Max-type equation | Positive solution |
Publisher: | Elsevier |
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