Oscillation and Nonoscillation of Second Order Neutral Delay Difference Equations

Abstract

Some new oscillation and nonoscillation criteria for the second order neutral delay difference equation

$$\Delta \left( {c_n \Delta \left( {y_n {\text{ + }}p_n y_n - k} \right)} \right) + q_n y_{n + 1 - m}^\beta = 0,n \geqslant n_0 $$

where k, m are positive integers and β is a ratio of odd positive integers are established, under the condition ${\sum\limits_{n{\text{ = }}n_O }^\infty {1/c_n < } \;\infty }$