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This paper is concerned with the characterization of the linear higher-order neutral difference equations of the form (Er) ∆ (y(n)− py(n− s)) + (−1) m ∑ i=1 qiy(n− σi) = 0, r = 1 or 2 for |p| < ∞. Using the linearized oscillation method we have studied the oscillation of a class of nonlinear neutral difference equations of the form ∆(y(n)− p(n)g(y(n− s))) + m ∑ i=1 qi(n)hi(y(n− σi)) = 0 with respect to its associated linear difference equations (Er). AMS Subject Classifications: 39A10, 39A12.

Characterization of Higher-Order Neutral Difference Equations with Several Delays