Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
