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In this paper, we show the existence of function which is notS-asymptotically omega-periodic, but which is S-asymptotically omega-periodicin the Stepanov sense. We give sufficient conditions for the existence anduniqueness of S-asymptotically omega-periodic solutions for a nonautonomousdifferential equation with piecewise constant argument in a Banach space whenomega is an integer. This is done using the Banach fixed point Theorem. Anexample involving the heat operator is discussed as an illustration of thetheory.

S-asymptotically omega-periodic solution for a nonlinear differential  equation with piecewise constant argument via S-asymptotically omega-periodic  functions in the Stepanov sense