Multiplicity result for a mass supercritical NLS with a partial confinement
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929717946351616 |
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| author | Jeanjean, Louis Song, Linjie |
| author_facet | Jeanjean, Louis Song, Linjie |
| contents | We consider an NLS equation in $\mathbb{R}^3$ with partial confinement and mass supercritical nonlinearity. In Bellazzini, Boussaid, Jeanjean and Visciglia (Comm. Math. Phys. 353, 2017, 229-251) for such a problem, a solution with a prescribed $L^2$ norm was obtained, as a local minima, and the existence of a second solution, at a mountain pass energy level, was proposed as an open problem. We give here a positive, non-perturbative, answer to this problem. Our solution is obtained as a limit of a sequence of solutions of corresponding problems on bounded domains of $\mathbb{R}^3$. The symmetry of solutions on bounded domains is used centrally in the convergence process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11472 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiplicity result for a mass supercritical NLS with a partial confinement Jeanjean, Louis Song, Linjie Analysis of PDEs 35A15, 35J60 We consider an NLS equation in $\mathbb{R}^3$ with partial confinement and mass supercritical nonlinearity. In Bellazzini, Boussaid, Jeanjean and Visciglia (Comm. Math. Phys. 353, 2017, 229-251) for such a problem, a solution with a prescribed $L^2$ norm was obtained, as a local minima, and the existence of a second solution, at a mountain pass energy level, was proposed as an open problem. We give here a positive, non-perturbative, answer to this problem. Our solution is obtained as a limit of a sequence of solutions of corresponding problems on bounded domains of $\mathbb{R}^3$. The symmetry of solutions on bounded domains is used centrally in the convergence process. |
| title | Multiplicity result for a mass supercritical NLS with a partial confinement |
| topic | Analysis of PDEs 35A15, 35J60 |
| url | https://arxiv.org/abs/2502.11472 |