IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2013y2013i1n165382.html

Existence and Iterative Algorithms of Positive Solutions for a Higher Order Nonlinear Neutral Delay Differential Equation

Author

Listed:
  • Zeqing Liu
  • Ling Guan
  • Sunhong Lee
  • Shin Min Kang

Abstract

This paper is concerned with the higher order nonlinear neutral delay differential equation [a(t)(x(t) + b(t)x(t − τ)) (m)] (n−m) + [h(t, x(h1(t)), …, x(hl(t)))] (i) + f(t, x(f1(t)), …, x(fl(t))) = g(t), for all t ≥ t0. Using the Banach fixed point theorem, we establish the existence results of uncountably many positive solutions for the equation, construct Mann iterative sequences for approximating these positive solutions, and discuss error estimates between the approximate solutions and the positive solutions. Nine examples are included to dwell upon the importance and advantages of our results.

Suggested Citation

  • Zeqing Liu & Ling Guan & Sunhong Lee & Shin Min Kang, 2013. "Existence and Iterative Algorithms of Positive Solutions for a Higher Order Nonlinear Neutral Delay Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:165382
    DOI: 10.1155/2013/165382
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/165382
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/165382?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
    ---><---

    References listed on IDEAS

    as
    1. Zeqing Liu & Lin Chen & Shin Min Kang & Sun Young Cho, 2011. "Existence of Nonoscillatory Solutions for a Third‐Order Nonlinear Neutral Delay Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiumei Lv & Tengwei Shao & Jiacheng Chen, 2013. "The Study of the Solution to a Generalized KdV‐mKdV Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

    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. Zeqing Liu & Jingjing Zhu & Jeong Sheok Ume & Shin Min Kang, 2014. "Positive Solutions and Mann Iterations of a Fourth Order Nonlinear Neutral Delay Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Gao, Yin & Yang, Yilin & Tang, Han, 2025. "Stability in mean for uncertain multiple-delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    3. B. Dorociaková & M. Kubjatková & R. Olach, 2012. "Existence of Positive Solutions of Neutral Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

    More about this item

    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:wly:jnlaaa:v:2013:y:2013:i:1:n:165382. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.