IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v6y2018i3p40-d135295.html
   My bibliography  Save this article

Existence of Solution, Filippov’s Theorem and Compactness of the Set of Solutions for a Third-Order Differential Inclusion with Three- Point Boundary Conditions

Author

Listed:
  • Ali Rezaiguia

    (Department of Mathematics and Computer Science, Faculty of Sciences , University of Souk Ahras, Souk Ahras 41000, Algeria)

  • Smail Kelaiaia

    (Department of Mathematics, Faculty of Sciences, University of Annaba, P.O. Box 12, Annaba 23000, Algerie)

Abstract

In this paper, we study a third-order differential inclusion with three-point boundary conditions. We prove the existence of a solution under convexity conditions on the multi-valued right-hand side; the proof is based on a nonlinear alternative of Leray-Schauder type. We also study the compactness of the set of solutions and establish some Filippov’s- type results for this problem.

Suggested Citation

  • Ali Rezaiguia & Smail Kelaiaia, 2018. "Existence of Solution, Filippov’s Theorem and Compactness of the Set of Solutions for a Third-Order Differential Inclusion with Three- Point Boundary Conditions," Mathematics, MDPI, vol. 6(3), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:3:p:40-:d:135295
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/6/3/40/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/6/3/40/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. M. Benchohra & S. K. Ntouyas, 2000. "Controllability of Second-Order Differential Inclusions in Banach Spaces with Nonlocal Conditions," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 559-571, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. M. Guo & X. Xue & R. Li, 2004. "Controllability of Impulsive Evolution Inclusions with Nonlocal Conditions," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 355-374, February.
    2. M. Benchohra & S. K. Ntouyas, 2001. "Controllability for an Infinite-Time Horizon of Second-Order Differential Inclusions in Banach Spaces with Nonlocal Conditions," Journal of Optimization Theory and Applications, Springer, vol. 109(1), pages 85-98, April.
    3. Y. K. Chang & W. T. Li, 2006. "Controllability of Second-Order Differential and Integro-Differential Inclusions in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 77-87, April.
    4. Li, Meili & Wang, Miansen & Zhang, Fengqin, 2006. "Controllability of impulsive functional differential systems in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 175-181.

    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:gam:jmathe:v:6:y:2018:i:3:p:40-:d:135295. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.