OSCILLATION THEOREM FOR SECOND-ORDER DIFFERENCE EQUATIONS

Sufficient and necessary conditions are established for the secondorder difference equations $\Delta \left( {{r_{n - 1}}\Delta {x_{n - 1}}} \right) + {p_n}x_n^\gamma = 0,n = 1,2,...$ where γ is the quotient of odd positive integers. Our results extend the well known oscillation theorem which was proved in [1,JMAA,91:9-29,1983], and answer an open problem in [2] when rn = 1, γ = 1.