IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-1596-7_5.html
   My bibliography  Save this book chapter

Bounded Saddle Point Methods

In: Linking Methods in Critical Point Theory

Author

Listed:
  • Martin Schechter

    (University of California, Department of Mathematics)

Abstract

Although a critical sequence does not necessarily lead to a critical point, we saw in Chapter III (cf. Theorem 3.4.1) that in some applications, bounded critical sequences do indeed lead to critical points. Thus one might ask if there are criteria that can be imposed which will produce bounded critical sequences. We study this question in Section 5.2. There we require the two linking sets A, B to be contained in a ball of radius R and impose a boundary condition on the sphere comprising the boundary of the ball to prevent deformations of the sets from exiting the ball. We then show that this indeed produces a bounded Palais-Smale sequence. However, the boundary condition is an additional restriction which asserts itself in the applications. As we shall see in Section 5.8, the restriction is not as severe as those used to cause a Palais-Smale sequence to be bounded. Consequently, the boundary condition pays for itself in applications.

Suggested Citation

  • Martin Schechter, 1999. "Bounded Saddle Point Methods," Springer Books, in: Linking Methods in Critical Point Theory, chapter 0, pages 99-130, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1596-7_5
    DOI: 10.1007/978-1-4612-1596-7_5
    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:978-1-4612-1596-7_5. 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.