The Global Attractivity of the Rational Difference
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چکیده
This paper studies the behavior of positive solutions of the recursive equation yn = 1 + yn−k yn−m , n = 0, 1, 2, . . . , with y−s, y−s+1, . . . , y−1 ∈ (0,∞) and k, m ∈ {1, 2, 3, 4, . . .}, where s = max{k, m}. We prove that if gcd(k, m) = 1, with k odd, then yn tends to 2, exponentially. When combined with a recent result in E. A. Grove, and G. Ladas, Periodicities in Nonlinear Difference Equations, Chapman & Hall/CRC Press, Boca Raton, (2004), this answers the question when y = 2 is a global attractor.
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تاریخ انتشار 2005