1 . The proof is based on the virial inequality of Kowalczyk et al., J. Eur. Math. Soc. (JEMS) 24 (2022), with smoothing estimates as shown in Mizumachi J. Math. Kyoto Univ. 48 (2008)."> 1 . The proof is based on the virial inequality of Kowalczyk et al., J. Eur. Math. Soc. (JEMS) 24 (2022), with smoothing estimates as shown in Mizumachi J. Math. Kyoto Univ. 48 (2008).">
[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i24p3876-d1540070.html
   My bibliography  Save this article

On Small Energy Solutions of the Nonlinear Schrödinger Equation in 1D with a Generic Trapping Potential with a Single Eigenvalue

Author

Listed:
  • Scipio Cuccagna

    (Department of Mathematics, Informatics and Geosciences, University of Trieste, Via Valerio 12/1, 34127 Trieste, Italy)

  • Masaya Maeda

    (Department of Mathematics and Informatics, Graduate School of Science, Chiba University, Chiba 263-8522, Japan)

Abstract
We prove in dimension d = 1 a result similar to a classical paper by Soffer and Weinstein, Jour. Diff. Eq. 98 (1992), improving it by encompassing for pure power nonlinearities the whole range of exponents p > 1 . The proof is based on the virial inequality of Kowalczyk et al., J. Eur. Math. Soc. (JEMS) 24 (2022), with smoothing estimates as shown in Mizumachi J. Math. Kyoto Univ. 48 (2008).

Suggested Citation

  • Scipio Cuccagna & Masaya Maeda, 2024. "On Small Energy Solutions of the Nonlinear Schrödinger Equation in 1D with a Generic Trapping Potential with a Single Eigenvalue," Mathematics, MDPI, vol. 12(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3876-:d:1540070
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/24/3876/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/24/3876/
    Download Restriction: no
    ---><---

    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:12:y:2024:i:24:p:3876-:d:1540070. 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: 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.