International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2002 / Article

Open Access

Volume 15 |Article ID 681080 | 10 pages |

Periodic solutions of non-densely defined delay evolution equations

Received01 Jul 2000
Revised01 May 2001


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.

64 Views | 386 Downloads | 16 Citations
 PDF  Download Citation  Citation
 Order printed copiesOrder

We are committed to sharing findings related to COVID-19 as quickly and safely as possible. Any author submitting a COVID-19 paper should notify us at to ensure their research is fast-tracked and made available on a preprint server as soon as possible. We will be providing unlimited waivers of publication charges for accepted articles related to COVID-19. Sign up here as a reviewer to help fast-track new submissions.