IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v143y2009i2d10.1007_s10957-009-9564-x.html
   My bibliography  Save this article

Approximate Controllability of Second-Order Stochastic Distributed Implicit Functional Differential Systems with Infinite Delay

Author

Listed:
  • P. Balasubramaniam

    (Gandhigram Rural University)

  • P. Muthukumar

    (Gandhigram Rural University)

Abstract

In this paper, sufficient conditions for the approximate controllability of the following stochastic semilinear abstract functional differential equations with infinite delay are established $$\begin{array}{@{}l@{}}d\bigl[x^{\prime}(t)-g(t,x_{t})\bigr]=\bigl[Ax(t)+f(t,x_{t})+Bu(t)\bigr]dt+G(t,x_{t})dW(t),\\\noalign{\vskip3pt}\quad \mbox{a.e on}\ t\in J:=[0,b],\\\noalign{\vskip3pt}x_{0}=\varphi\in {\mathfrak{B}},\\\noalign{\vskip3pt}x^{\prime}(0)=\psi \in H,\end{array}$$ where the state x(t)∈H,x t belongs to phase space ${\mathfrak{B}}$ and the control u(t)∈L 2 ℱ (J,U), in which H,U are separable Hilbert spaces and d is the stochastic differentiation. The results are worked out based on the comparison of the associated linear systems. An application to the stochastic nonlinear wave equation with infinite delay is given.

Suggested Citation

  • P. Balasubramaniam & P. Muthukumar, 2009. "Approximate Controllability of Second-Order Stochastic Distributed Implicit Functional Differential Systems with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 225-244, November.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:2:d:10.1007_s10957-009-9564-x
    DOI: 10.1007/s10957-009-9564-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-009-9564-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-009-9564-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Y. Ren & D. D. Sun, 2010. "Second-order Neutral Stochastic Evolution Equations with Infinite Delay under Carathéodory Conditions," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 569-582, December.
    2. Ren, Yong & Hou, Tingting & Sakthivel, R. & Cheng, Xing, 2014. "A note on the second-order non-autonomous neutral stochastic evolution equations with infinite delay under Carathéodory conditions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 658-665.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:143:y:2009:i:2:d:10.1007_s10957-009-9564-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.