Global Behavior of Solutions of a Nonlinear Second-Order Difference Equation

Our aim in this paper is to investigate the boundedness, the persistence, the global attractivity, the existence of periodic solutions of period 2, and the oscillatory nature of solutions of the equation xnq1sf xn, xny1., ns0, 1, . . . , where f is a continuous, positive, and decreasing function on w0, `.2 _ 0, 0.4. The results are applied to the difference equation A 1 ynq1synpqynqy1 , ns0, 1, . . . , where A, p, qg 0, `..