Abstract

We investigate scalar impulsive differential equations with piecewise constant generalized mixed arguments, abbreviated as the IDEPCAG of mixed type. These equations have general step functions as arguments. We propose criteria for the existence of oscillatory and non-oscillatory solutions, and obtain sufficient conditions for the stability of the zero solution. Our results are novel, and extend and improve upon previous publications. Additionally, we provide several numerical examples and simulations to demonstrate the feasibility of our findings.