{"paper":{"title":"Semiclassical stationary states for nonlinear Schr\\\"odinger equations under a strong external magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean Van Schaftingen, Jonathan Di Cosmo","submitted_at":"2013-12-19T10:24:19Z","abstract_excerpt":"We construct solutions to the nonlinear magnetic Schr\\\"odinger equation $$\n  \\left\\{ \\begin{aligned}\n  - \\varepsilon^2 \\Delta_{A/\\varepsilon^2} u + V u &= \\lvert u\\rvert^{p-2} u & &\\text{in}\\ \\Omega,\\\\ u &= 0 & &\\text{on}\\ \\partial\\Omega,\n  \\end{aligned}\n  \\right. $$ in the semiclassical r\\'egime with strong magnetic fields. In contrast with the well-studied mild magnetic field r\\'egime, the limiting energy depends on the magnetic field allowing to recover the Lorentz force in the semi-classical limit. Our solutions concentrate around global or local minima of a limiting energy that depends on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5467","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}