International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2001 / Article

Open Access

Volume 14 |Article ID 265389 | 12 pages |

On the stability of stationary solutions of a linear integro-differential equation

Received01 Oct 1999
Revised01 Nov 2000


In this paper the following two connected problems are discussed. The problem of the existence of a stationary solution for the abstract equation ϵx(t)+x(t)=Ax(t)+tE(ts)x(s)ds+ξ(t),tR containing a small parameter ϵ in Banach space B is considered. Here A(B) is a fixed operator, EC([0,+),(B)) and ξ is a stationary process. The asymptotic expansion of the stationary solution for equation (1) in the series on degrees of e is given.We have proved also the existence of a stationary with respect to time solution of the boundary value problem in B for a telegraph equation (6) containing the small parameter ϵ. The asymptotic expansion of this solution is also obtained.

Copyright © 2001 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.

101 Views | 241 Downloads | 1 Citation
 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.