Authors: | Stević, Stevo | Title: | A note on periodic character of a difference equation | Journal: | Journal of Difference Equations and Applications | Volume: | 10 | Issue: | 10 | First page: | 929 | Last page: | 932 | Issue Date: | 20-Aug-2004 | Rank: | M22 | ISSN: | 1023-6198 | DOI: | 10.1080/10236190412331272616 | Abstract: | In this note, we study positive solutions of the difference equation x n+1 = p + x n-(2s-1) /x n-(2l+1)s+1 , n = 0, 1... where p ∈ [1, ∞) and s, l ∈ N. We prove that if p > 1, then every positive solution converges to the positive equilibrium x* = p + 1 and if p = 1, then every positive solution converges to a 2s-periodic solution. The second result generalizes the main result in the paper: W.T. Patula and H.D.Voulov, On the oscillation and periodic character of a third order rational difference equation, Proc. Amer. Math. Soc. 131 (3) (2003), 905-909. |
Keywords: | Difference equation | Period two solution | Periodic character | Positive solution | Publisher: | Taylor & Francis |
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