{"paper":{"title":"Existence of non-topological solutions for a skew-symmetric Chern-Simons system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Genggeng Huang","submitted_at":"2014-01-07T00:47:17Z","abstract_excerpt":"We investigate the existence of non-topological solutions $(u_1,u_2)$ satisfying\n  $$u_{i}(x)=-2\\beta_i\\ln|x|+O(1),\\quad\\text{as }|x|\\rightarrow +\\infty,$$ such that $\\beta_i>1$ and\n  $$(\\beta_1-1)(\\beta_2-1)>(N_1+1)(N_2+1),$$\n  for a skew-symmetric Chern-Simons system. By the bubbling analysis and the Leray-Schauder degree theory, we get the existence results except for a finite set of curves: $$\\frac{N_1}{\\beta_1+N_1}+\\frac{N_2}{\\beta_2+N_2}=\\frac{k-1}{k},k=2,\\cdots,\\max(N_1,N_2).$$ This generalizes a previous work by Choe-Kim-Lin \\cite{ChoeKimLin2011}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1251","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"}