Normalized solutions of nonlinear magnetic Schrödinger equations on 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_ | 1866915698066849792 |
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| author | d'Avenia, Pietro He, Zhentao Ji, Chao |
| author_facet | d'Avenia, Pietro He, Zhentao Ji, Chao |
| contents | In this paper we first establish the theory of a magnetic Sobolev space $H^1_A(\mathcal{G},\mathbb{C})$ on metric graphs $\mathcal{G}$ and we prove the self-adjointness of its corresponding magnetic Schrödinger operator. Then, in this setting, we investigate the existence and multiplicity of normalized solutions to nonlinear magnetic Schrödinger equations on compact metric graphs and on noncompact metric graphs with localized nonlinearities or nonlinearities acting on whole metric graphs, covering the mass-subcritical, mass-critical, and mass-supercritical cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normalized solutions of nonlinear magnetic Schrödinger equations on metric graphs d'Avenia, Pietro He, Zhentao Ji, Chao Analysis of PDEs 35R02, 81Q35, 78M30, 35Q40 In this paper we first establish the theory of a magnetic Sobolev space $H^1_A(\mathcal{G},\mathbb{C})$ on metric graphs $\mathcal{G}$ and we prove the self-adjointness of its corresponding magnetic Schrödinger operator. Then, in this setting, we investigate the existence and multiplicity of normalized solutions to nonlinear magnetic Schrödinger equations on compact metric graphs and on noncompact metric graphs with localized nonlinearities or nonlinearities acting on whole metric graphs, covering the mass-subcritical, mass-critical, and mass-supercritical cases. |
| title | Normalized solutions of nonlinear magnetic Schrödinger equations on metric graphs |
| topic | Analysis of PDEs 35R02, 81Q35, 78M30, 35Q40 |
| url | https://arxiv.org/abs/2512.23321 |