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

2017/11/10 by William Dimbour, Dimbour, William, Solym Manou-Abi +2
Engineering · Mathematics · #34A12 #34A40 #34K05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fixed Point Theorems Analysis #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1711.03768

openalex publication_date 2017/11/10 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

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

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