IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v184y2020i3d10.1007_s10957-019-01584-x.html
   My bibliography  Save this article

Sturm–Liouville Problems Involving Distribution Weights and an Application to Optimal Problems

Author

Listed:
  • Hongjie Guo

    (Shandong University at Weihai
    Swinburne University of Technology)

  • Jiangang Qi

    (Shandong University at Weihai)

Abstract

This paper is concerned with Sturm–Liouville problems (SLPs) with distribution weights and sets up the min–max principle and Lyapunov-type inequality for such problems. As an application, the paper solves the following optimization problems: If the first eigenvalue of a string vibration problem is known, what is the minimal total mass and by which distribution of weight is it attained; if both the first eigenvalue and the total mass are known, what is the corresponding results on the string mass? The vibration problem leads to a SLP with the spectral parameter in both the equation and the boundary conditions. Our main method is to incorporate this problem into the framework of classical SLPs with weights in an appropriate space by transforming it into the one with distribution weight, which provides a different idea for the investigation of the SLPs with spectral parameter in boundary condition.

Suggested Citation

  • Hongjie Guo & Jiangang Qi, 2020. "Sturm–Liouville Problems Involving Distribution Weights and an Application to Optimal Problems," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 842-857, March.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:3:d:10.1007_s10957-019-01584-x
    DOI: 10.1007/s10957-019-01584-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-019-01584-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/s10957-019-01584-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. Elena Corina Cipu & Cosmin Dănuţ Barbu, 2022. "Variational Estimation Methods for Sturm–Liouville Problems," Mathematics, MDPI, vol. 10(20), pages 1-18, October.

    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:184:y:2020:i:3:d:10.1007_s10957-019-01584-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.