The Behavior of Positive Solutions of a Nonlinear Second-Order Difference Equation

This paper studies the boundedness, global asymptotic stability, and periodicity of positive solutions of the equation xn f xn−2 /g xn−1 , n ∈ N0, where f, g ∈ C 0,∞ , 0,∞ . It is shown that if f and g are nondecreasing, then for every solution of the equation the subsequences {x2n} and {x2n−1} are eventually monotone. For the case when f x α βx and g… CONTINUE READING