Oscillation Criteria for Hybrid Second-Order Neutral Delay Difference Equations with Mixed Coefficients

This paper explores the oscillatory behavior of a class of second-order hybrid-type neutral delay difference equations. A novel approach is introduced to transform these complex trinomial equations into a simpler binomial form by utilizing solutions from an associated linear difference equation. By employing comparison techniques and summation-averaging methods, we establish new oscillation criteria which guarantee that all solutions exhibit oscillatory behavior. Our findings extend to an existing oscillation theory and are applicable even to non-neutral second-order equations. A couple of examples are presented to highlight the impact and novelty of the obtained results.