Document Type

Article

Publication Date

1988

Publication Source

International Journal of Mathematics and Mathematical Sciences

Abstract

Consider the system of equations

x(t)=f(t)+∫−∞tk(t,s)x(s)ds,           (1)

and

x(t)=f(t)+∫−∞tk(t,s)g(s,x(s))ds.        (2)

Existence of continuous periodic solutions of (1) is shown using the resolvent function of the kernel k. Some important properties of the resolvent function including its uniqueness are obtained in the process. In obtaining periodic solutions of (1) it is necessary that the resolvent of k is integrable in some sense. For a scalar convolution kernel k some explicit conditions are derived to determine whether or not the resolvent of k is integrable. Finally, the existence and uniqueness of continuous periodic solutions of (1) and (2) are obtained using the contraction mapping principle as the basic tool.

Inclusive pages

781-792

ISBN/ISSN

0161-1712

Document Version

Published Version

Comments

This document has been made available for download in accordance with the publisher's policy on self-archiving.

Permission documentation on file.

Publisher

Hindawi Publishing Corp.

Volume

11

Issue

4

Place of Publication

Cairo, Egypt

Peer Reviewed

yes

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