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Periodicity and continuous dependence in iterative differential equations

10$
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Periodicity and continuous dependence in iterative differential equations

10$

Bouzid Mansouri, Abdelouaheb Ardjouni & Ahcene Djoudi 

Abstract

In this work, we study the existence, uniqueness and continuous dependence of periodic solutions of the iterative differential equation

x′(t)=∑m=1N∑l=1∞Cl,m(t)(x[m](t))l+ddtg(t,x[1](t),x[2](t),…,x[N](t))+h(t).x′(t)=∑m=1N∑l=1∞Cl,m(t)(x[m](t))l+ddtg(t,x[1](t),x[2](t),…,x[N](t))+h(t).

Using Schauder’s fixed point theorem, we obtain the existence of periodic solution and by the contraction mapping principle we obtain the uniqueness. An example is given to illustrate this work. The results obtained here extend the work of Zhao and Feckan [14].

Only units of this product remain
Year 2020
Language English
Format PDF
DOI 10.1007/s12215-019-00420-5