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Normalized solutions to the Schrödinger equations with van der Waals type potentials.

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Title: Normalized solutions to the Schrödinger equations with van der Waals type potentials.
Authors: Wang, Zhi-Jie1 (AUTHOR) wangzhj2020@lzu.edu.cn, Sun, Hong-Rui1 (AUTHOR) hrsun@lzu.edu.cn
Source: Zeitschrift für Angewandte Mathematik und Physik (ZAMP). Oct2025, Vol. 76 Issue 5, p1-30. 30p.
Subjects: Schrödinger equation, Equations, Lagrange multiplier
Abstract: In this paper, we focus on the solutions to the following Schrödinger equations with van der Waals type potentials - Δ u + V (x) u = λ u + μ (| x | - α ∗ | u | 2 ) u + (| x | - 4 ∗ | u | 2) u , x ∈ R N with prescribed mass ∫ R N | u | 2 d x = c 2 , where N ⩾ 5 , μ , c > 0 , 0 < α < 4 , V is an external potential vanishing at infinity, and the parameter λ ∈ R appears as a Lagrange multiplier. Under some explicit assumptions on V, we prove the existence of normalized solutions for the above problem. [ABSTRACT FROM AUTHOR]
Copyright of Zeitschrift für Angewandte Mathematik und Physik (ZAMP) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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  Data: In this paper, we focus on the solutions to the following Schr&#246;dinger equations with van der Waals type potentials - Δ u + V (x) u = λ u + μ (| x | - α ∗ | u | 2 ) u + (| x | - 4 ∗ | u | 2) u , x ∈ R N with prescribed mass ∫ R N | u | 2 d x = c 2 , where N ⩾ 5 , μ , c &gt; 0 , 0 &lt; α &lt; 4 , V is an external potential vanishing at infinity, and the parameter λ ∈ R appears as a Lagrange multiplier. Under some explicit assumptions on V, we prove the existence of normalized solutions for the above problem. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: &lt;i&gt;Copyright of Zeitschrift f&#252;r Angewandte Mathematik und Physik (ZAMP) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
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    Identifiers:
      – Type: doi
        Value: 10.1007/s00033-025-02572-0
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      – Code: eng
        Text: English
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        PageCount: 30
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    Subjects:
      – SubjectFull: Schrödinger equation
        Type: general
      – SubjectFull: Equations
        Type: general
      – SubjectFull: Lagrange multiplier
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      – TitleFull: Normalized solutions to the Schrödinger equations with van der Waals type potentials.
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            NameFull: Wang, Zhi-Jie
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            – D: 01
              M: 10
              Text: Oct2025
              Type: published
              Y: 2025
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