Authors: | Stević, Stevo | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | On the rational (k + 1, k + 1)-type difference equation | Journal: | Journal of Applied Mathematics and Computing | Volume: | 24 | Issue: | 1-2 | First page: | 295 | Last page: | 303 | Issue Date: | 1-May-2007 | ISSN: | 1598-5865 | DOI: | 10.1007/BF02832318 | Abstract: | In this paper we investigate the boundedness character of the positive solutions of the rational difference equation of the form xn+1 = a 0 + ∑ j=1k a jx n-j+1/b 0 + ∑ j=1k a jx n-j+1. n= 0,1,... where k ∈ N, and a j, b j, j = 0, 1,... ,k, are nonnegative numbers such that b 0 + + ∑ j=1k a jx n-j+1 > 0 for every n ∈ N∪{0}. In passing we confirm several conjectures recently posed in the paper: E. Camouzis, G. Ladas and E. P. Quinn, On third order rational difference equations (part 6), J. Differ. Equations Appl. 11(8) (2005), 759-777. |
Keywords: | Boundedness | Difference equation | Global attractivity | Positive solutions | Publisher: | Springer Link |
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