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

TL;DR

This paper establishes the existence and uniqueness of S-asymptotically omega-periodic solutions in the Stepanov sense for a class of nonlinear differential equations with piecewise constant argument, using fixed point methods.

Contribution

It introduces new conditions for solutions that are S-asymptotically omega-periodic in the Stepanov sense, expanding the understanding of periodic solutions in differential equations.

Findings

Existence of non-S-asymptotically omega-periodic functions in Stepanov sense.

Sufficient conditions for unique solutions in Banach spaces.

Application to heat operator example.

Abstract

In this paper, we show the existence of function which is not S-asymptotically omega-periodic, but which is S-asymptotically omega-periodic in the Stepanov sense. We give sufficient conditions for the existence and uniqueness of S-asymptotically omega-periodic solutions for a nonautonomous differential equation with piecewise constant argument in a Banach space when omega is an integer. This is done using the Banach fixed point Theorem. An example involving the heat operator is discussed as an illustration of the theory.