IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-94-017-2515-6_5.html
   My bibliography  Save this book chapter

Oscillation Theory for Sublinear Differential Equations

In: Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations

Author

Listed:
  • Ravi P. Agarwal

    (Florida Institute of Technology)

  • Said R. Grace

    (Cairo University)

  • Donal O’Regan

    (National University of Ireland)

Abstract

In this chapter we shall present oscillation and nonoscillation criteria for all solutions of second order nonlinear differential equations of sublinear type with alternating coefficients. In Section 5.1, our sublinear oscillation results involve integrals and weighted integrals of the alternating coefficients. In some results we employ integral averaging techniques. In Section 5.2, we impose some additional conditions on the sublinear term which allow us to proceed further and extend and improve several known theorems in the literature. In fact, we make an asymptotic study which results in new oscillation criteria. Section 5.3 provides some new linearized oscillation results for second order sublinear differential equations. In Section 5.4, we shall present criteria for the nonoscillation of sublinear Emden-Fowler type equations. In Section 5.5, we compare the oscillatory behavior of certain nonlinear equations with the related half-linear differential equations. Here oscillation of general nonlinear differential equations is also discussed.

Suggested Citation

  • Ravi P. Agarwal & Said R. Grace & Donal O’Regan, 2002. "Oscillation Theory for Sublinear Differential Equations," Springer Books, in: Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations, chapter 0, pages 376-456, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-2515-6_5
    DOI: 10.1007/978-94-017-2515-6_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:978-94-017-2515-6_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.