IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v294y2021i8p1595-1628.html
   My bibliography  Save this article

Well‐posedness for fully nonlinear functional differential equations

Author

Listed:
  • Naoki Tanaka

Abstract

This paper deals with the well‐posedness for the fully nonlinear functional differential equation u′(t)∈A(t)ut in a general Banach space X, where {A(t);t∈[a,b)} is a family of operators whose domains are subsets of the so‐called initial‐history space X and whose ranges are subsets of the space X. The special case where A(t)ϕ=B(t)ϕ(0)+G(t,ϕ) for t∈[a,b) and ϕ∈X with ϕ(0)∈D(B(t)) has been extensively studied so far, but there has not been a satisfactory solution to the flow invariance problem. This paper establishes the well‐posedness for the fully nonlinear functional differential equations and solves the above‐mentioned problem on flow invariance.

Suggested Citation

  • Naoki Tanaka, 2021. "Well‐posedness for fully nonlinear functional differential equations," Mathematische Nachrichten, Wiley Blackwell, vol. 294(8), pages 1595-1628, August.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:8:p:1595-1628
    DOI: 10.1002/mana.201800498
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.201800498
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mana.201800498?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
    ---><---

    More about this item

    Statistics

    Access and download statistics

    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:bla:mathna:v:294:y:2021:i:8:p:1595-1628. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0025-584X .

    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.