Periodica Mathematica Hungarica, cilt.87, sa.1, ss.265-277, 2023 (SCI-Expanded)
© 2023, Akadémiai Kiadó, Budapest, Hungary.In this paper, we consider a first order neutral differential equation with piecewise constant mixed arguments. We show the existence and uniqueness of solutions of the equation together a given initial condition. Moreover, for the considered equation we establish the conditions of oscillatory and convergency. We also give some examples that illustrate our results.