{"paper":{"title":"Multiple solutions for a NLS equation with critical growth and magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Giovany M. Figueiredo","submitted_at":"2013-04-17T11:06:48Z","abstract_excerpt":"In this paper, we are concerned with the multiplicity of nontrivial solutions for the following class of complex problems $$ (-i\\nabla - A(\\mu x))^{2}u= \\mu |u|^{q-2}u + |u|^{2^{*}-2}u \\ \\mbox{in} \\ \\Omega, \\ \\ \\ \\ u \\in H^{1}_{0}(\\Omega,\\mathbb{C}), $$ where $\\Omega \\subset \\mathbb{R}^{N} (N \\geq 4)$ is a bounded domain with smooth boundary. Using the Lusternik-Schnirelman theory, we relate the number of solutions with the topology of $\\Omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4767","kind":"arxiv","version":1},"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"}