Title
Periodic Solutions of Neutral Nonlinear Systems of Differential Equations with Functional Delay
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
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
COinS
Comments
Permission documentation on file.