Periodic solutions by Krasnoselskii fixed point theorem of neutral nonlinear system of dynamical equation with Variable Delays

A.A. Ben Fayed¹ , H.A. Makhzoum² , R.A. Elmansouri³ , A.K. Alshaikhly⁴

Section:Research Paper, Product Type: Journal-Paper
Vol.8 , Issue.5 , pp.27-32, Oct-2021

Online published on Oct 31, 2021

Copyright © A.A. Ben Fayed, H.A. Makhzoum, R.A. Elmansouri, A.K. Alshaikhly . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The aim of this work to investigate the existence and uniqueness of periodic solutions of the nonlinear neutral system of differential equations by employing Krasnoselskii`s fixed point theorem under slightly more stringent conditions and by applying the solution of the fundamental matrix solution of y`= A(t)y. This is accomplished by transforming the given neutral system differential equation into an equivalent integral equation that allows for the construction of suitable mappings, one of which is a contraction and the other which is compact, both of which allow for the proof of the existence of periodic solutions. Moreover, it was demonstrated that there is a unique periodic solution to the nonlinear neutral system of differential equations by providing some sufficient conditions that can be used to assist in implementing the contraction mapping principle on the nonlinear neutral system of differential equations.

Key-Words / Index Term :
Krasnoselskii; Neutral differential equation; nonlinear equation; Integral equation; Periodic solution

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