Sign-changing prescribed mass solutions for $L^2$-supercritical NLS on compact metric graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912984519933952 |
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| author | Jeanjean, Louis Song, Linjie |
| author_facet | Jeanjean, Louis Song, Linjie |
| contents | This paper is devoted to the existence of multiple sign-changing solutions of prescribed mass for a mass-supercritical nonlinear Schrödinger equation set on a compact metric graph. In particular, we obtain, in the supercritical mass regime, the first multiplicity result for prescribed mass solutions on compact metric graphs. As a byproduct, we prove that any eigenvalue of the associated linear operator is a bifurcation point. Our approach relies on the introduction a new kind of link and on the use of gradient flow techniques on a constraint. It can be transposed to other problems posed on a bounded domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sign-changing prescribed mass solutions for $L^2$-supercritical NLS on compact metric graphs Jeanjean, Louis Song, Linjie Analysis of PDEs 35A15, 35J60 This paper is devoted to the existence of multiple sign-changing solutions of prescribed mass for a mass-supercritical nonlinear Schrödinger equation set on a compact metric graph. In particular, we obtain, in the supercritical mass regime, the first multiplicity result for prescribed mass solutions on compact metric graphs. As a byproduct, we prove that any eigenvalue of the associated linear operator is a bifurcation point. Our approach relies on the introduction a new kind of link and on the use of gradient flow techniques on a constraint. It can be transposed to other problems posed on a bounded domain. |
| title | Sign-changing prescribed mass solutions for $L^2$-supercritical NLS on compact metric graphs |
| topic | Analysis of PDEs 35A15, 35J60 |
| url | https://arxiv.org/abs/2501.14642 |