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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.04893 |
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Table of Contents:
- In this paper, we consider the existence and multiplicity of prescribed mass solutions to the following nonlinear Schrödinger equation with general nonlinearity: Mass super-critical case: \[\begin{cases} -Δu+V(x)u+λu=g(u),\\ \|u\|_2^2=\int|u|^2\mathrm{d}x=c, \end{cases} \] both on large bounded smooth star-shaped domain $Ω\subset\mathbb{R}^N$ and on $\mathbb{R}^N$, where $V(x)$ is the potential and the nonlinearity $g(\cdot)$ considered here are very general and of mass super-critical. The standard approach based on the Pohozaev identity to obtain normalized solutions is invalid as the presence of potential $V(x)$. In addition, our study can be considered as a complement of Bartsch-Qi-Zou (Math Ann 390, 4813--4859, 2024), which has addressed an open problem raised in Bartsch et al. (Commun Partial Differ Equ 46(9):1729--1756, 2021).