Analysis of Oscillatory Behavior of Second-Order Neutral Delay Difference Equations

The paper investigates the oscillation, zero-convergence, and solutions of second-order neutral delay difference equations containing three nonlinear delayed terms with different growth rates. By using positivity and monotonicity conditions on an auxiliary function along with divergence-type conditions on the coefficient sequences of the neutral and delayed terms, the paper establishes new criteria that guarantee oscillation or convergence of all solutions. These novel findings extend and enhance several of the existing oscillation criteria established by the literature. Suggestions for further investigation are included with illustrative examples.