Oscillation Results Using Linearization of Quasi-Linear Second Order Delay Difference Equations

In this paper, the authors investigate the oscillatory behavior of quasilinear second order delay difference equations of the form Δ ( b ( n ) ( Δ u ( n ) ) α ) + p ( n ) u β ( n - σ ) = 0 . By obtaining new monotonic properties of the nonoscillatory solutions and using them to linearize the equation leads to new oscillation criteria. The criteria obtained improve existing ones in the literature. Two examples are included to show the importance of the main results.