In this paper, sufficient conditions are obtained for nonoscillation/oscillation of all solutions of a class of nonlinear third order difference equations of the form a p n 2 a y n + q n 2 a y n = f n, y n , a y n , 2 a y n involving the generalized difference operator a which is defined as a y n = y n+1 − ay n , a = 0.

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ABSTRACT. In this paper, we obtain asymptotic bounds, under appropriate conditions, of solutions of third order difference equations of the formwhere {p n } and {r n } are sequences of positive real numbers, and f, g : N×R 2 → R. Different forms of discrete Gronwall inequality are used to obtain these results.