A global behavior of the positive solutions of xn+1 = A + Bxn + xn-2/βxn + xn-2

초록

In this paper we prove that every positive solution of the third order rational difference equation x<inf>n+1</inf> = βx<inf>n</inf> + x<inf>n-2</inf>/A + Bx<inf>n</inf> + x<inf>n-2</inf> converges to the positive equilibrium point x̄ = β + 1 - A/B + 1, where 0 < β ≤ B, 1 < A < β + 1. © 2008 The Korean Mathematical Society.

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