Oscillation Detection in Difference Equations with Several Non-Monotone Advanced Arguments via a New Approach

We investigate the oscillatory behavior of a first-order difference equation with several advanced arguments. New sufficient conditions for oscillation are established, and we show, through carefully constructed counterexamples, that many well-known criteria for equations with a single advanced argument fail to generalize to the several-argument setting, even when each advanced argument is increasing. Several illustrative examples are also provided to demonstrate the sharpness and practical effectiveness of the obtained con- ditions and to highlight their clear improvements over all existing results in the literature