Periodic Solutions of Neutral Nonlinear Systems of Differential Equations with Functional Delay

Author(s)

Muhammad Islam, University of DaytonFollow
Youssef Raffoul, University of DaytonFollow

Document Type

Article

Publication Date

7-15-2007

Publication Source

Journal of Mathematical Analysis and Applications

Abstract

We study the existence of periodic solutions of the nonlinear neutral system of differential equations of the form

(d/dt)x(t)=A(t)x(t)+(d/dt)Q(t,x(t−g(t)))+G(t,x(t),x(t−g(t))).

In the process we use the fundamental matrix solution of

y′=A(t)y

and convert the given neutral differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution of this neutral differential equation. We also use the contraction mapping principle to show the existence of a unique periodic solution of the equation.

Inclusive pages

1175-1186

ISBN/ISSN

0022-247X

Comments

Permission documentation on file.

Copyright

Copyright © 2007, Elsevier

Publisher

Elsevier

Volume

331

Issue

2

Place of Publication

Amsterdam, Netherlands

Peer Reviewed

yes

eCommons Citation

Islam, Muhammad and Raffoul, Youssef, "Periodic Solutions of Neutral Nonlinear Systems of Differential Equations with Functional Delay" (2007). Mathematics Faculty Publications. 59.
https://ecommons.udayton.edu/mth_fac_pub/59