IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-8176-8124-1_11.html
   My bibliography  Save this book chapter

Properties of the Leray-Schauder Degree

In: A Topological Introduction to Nonlinear Analysis

Author

Listed:
  • Robert F. Brown

    (University of California, Department of Mathematics)

Abstract

You may have noticed that once the Brouwer degree was defined and its properties established, we used it in the chapter that followed only in a sort of formal way. In defining the Leray-Schauder degree we needed to know that there was a well-defined integer, called the Brouwer degree, represented by the symbol d(I∈ - f∈, U∈), but we did not have to specify how that integer was defined. Furthermore, and this is the point I want to emphasize, in the proof that the Leray-Schauder degree is well-defined, which is really a theorem about the Brouwer degree, all we needed to know about that degree was two of its properties: homotopy and reduction of dimension. In this chapter, I will list and demonstrate properties of the Leray-Schauder degree; properties which, basically, are consequences of the corresponding properties of the Brouwer degree. Again all we will need to know about the Brouwer degree is its existence and properties. As in the previous chapter, no homology groups will ever appear. Then, once we have established these properties of the Leray-Schauder degree, that’s all we’ll need to know about that degree for the rest of the book. In other words, after this chapter we can forget how the degree was defined.

Suggested Citation

  • Robert F. Brown, 2004. "Properties of the Leray-Schauder Degree," Springer Books, in: A Topological Introduction to Nonlinear Analysis, edition 0, chapter 11, pages 69-78, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8124-1_11
    DOI: 10.1007/978-0-8176-8124-1_11
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:sprchp:978-0-8176-8124-1_11. 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.