A Note on Periodic Character of a Difference Equation.

In this note, we study positive solutions of the difference equation [This symbol cannot be presented in ASCII format] 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. [ABSTRACT FROM AUTHOR]