International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2002 / Article

Open Access

Volume 15 |Article ID 681080 | 10 pages | https://doi.org/10.1155/S1048953302000114

Periodic solutions of non-densely defined delay evolution equations

Received01 Jul 2000
Revised01 May 2001

Abstract

We study the finite delay evolution equation {x'(t)=Ax(t)+F(t,xt),t0,x0=ϕC([r,0],E), where the linear operator A is non-densely defined and satisfies the Hille-Yosida condition. First, we obtain some properties of “integral solutions” for this case and prove the compactness of an operator determined by integral solutions. This allows us to apply Horn's fixed point theorem to prove the existence of periodic integral solutions when integral solutions are bounded and ultimately bounded. This extends the study of periodic solutions for densely defined operators to the non-densely defined operators. An example is given.

Copyright © 2002 Hindawi Publishing Corporation. 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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