{"paper":{"title":"Multiple complex-valued solutions for nonlinear magnetic Schrodinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kazunaga Tanaka, Louis Jeanjean, Silvia Cingolani","submitted_at":"2016-04-21T05:53:43Z","abstract_excerpt":"We study, in the semiclassical limit, the singularly perturbed nonlinear Schr\\\"odinger equations $$ L^{\\hbar}_{A,V} u = f(|u|^2)u \\quad \\mbox{in } R^N $$ where $N \\geq 3$, $L^{\\hbar}_{A,V}$ is the Schr\\\"odinger operator with a magnetic field having source in a $C^1$ vector potential $A$ and a scalar continuous (electric) potential $V$ defined by \\begin{equation} L^{\\hbar}_{A,V}= -\\hbar^2 \\Delta-\\frac{2\\hbar}{i} A \\cdot \\nabla + |A|^2- \\frac{\\hbar}{i}\\operatorname{div}A + V(x). \\end{equation} Here $f$ is a nonlinear term which satisfies the so-called Berestycki-Lions conditions. We assume that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06188","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"}