{"paper":{"title":"Multiple solutions to a magnetic nonlinear Choquard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"M\\'onica Clapp, Silvia Cingolani, Simone Secchi","submitted_at":"2011-09-07T08:17:30Z","abstract_excerpt":"We consider the stationary nonlinear magnetic Choquard equation [(-\\mathrm{i}\\nabla+A(x))^{2}u+V(x)u=(\\frac{1}{|x|^{\\alpha}}\\ast |u|^{p}) |u|^{p-2}u,\\quad x\\in\\mathbb{R}^{N}%] where $A\\ $is a real valued vector potential, $V$ is a real valued scalar potential$,$ $N\\geq3$, $\\alpha\\in(0,N)$ and $2-(\\alpha/N) <p<(2N-\\alpha)/(N-2)$. \\ We assume that both $A$ and $V$ are compatible with the action of some group $G$ of linear isometries of $\\mathbb{R}^{N}$. We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition \\[ u(gx)=\\tau(g)u(x)\\text{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1386","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"}