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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2503.09262 |
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| _version_ | 1866915194545897472 |
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| author | Appolloni, Luigi Molle, Riccardo |
| author_facet | Appolloni, Luigi Molle, Riccardo |
| contents | We consider the problem $-Δu+λu=u^{p-1}$, where $u\in H^1_0(Ω)$ verifies $\|u\|_{L^2}=m>0$, and $λ\in [0,+\infty)$. Here, $\mathbb{R}^N\setminusΩ$ is nonempty and compact. We prove the existence of a solution with a constrained Morse index lower than or equal to $N+1$, both in the case $m$ fixed and $\mathbb{R}^N\setminusΩ$ in a small ball and in the case $Ω$ fixed and $m$ large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09262 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normalized Schrödinger equations with mass-supercritical nonlinearity in exterior domains Appolloni, Luigi Molle, Riccardo Analysis of PDEs 35J20 (Primary) 35J10, 35J91 (Secondary) We consider the problem $-Δu+λu=u^{p-1}$, where $u\in H^1_0(Ω)$ verifies $\|u\|_{L^2}=m>0$, and $λ\in [0,+\infty)$. Here, $\mathbb{R}^N\setminusΩ$ is nonempty and compact. We prove the existence of a solution with a constrained Morse index lower than or equal to $N+1$, both in the case $m$ fixed and $\mathbb{R}^N\setminusΩ$ in a small ball and in the case $Ω$ fixed and $m$ large. |
| title | Normalized Schrödinger equations with mass-supercritical nonlinearity in exterior domains |
| topic | Analysis of PDEs 35J20 (Primary) 35J10, 35J91 (Secondary) |
| url | https://arxiv.org/abs/2503.09262 |