{"paper":{"title":"Nonradial entire solutions for Liouville systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Gladiali, Luca Battaglia, Massimo Grossi","submitted_at":"2017-01-11T12:27:32Z","abstract_excerpt":"We consider the following system of Liouville equations: $$\\left\\{\\begin{array}{ll}-\\Delta u_1=2e^{u_1}+\\mu e^{u_2}&\\text{in }\\mathbb R^2\\\\-\\Delta u_2=\\mu e^{u_1}+2e^{u_2}&\\text{in }\\mathbb R^2\\\\\\int_{\\mathbb R^2}e^{u_1}<+\\infty,\\int_{\\mathbb R^2}e^{u_2}<+\\infty\\end{array}\\right.$$ We show existence of at least $n-\\left[\\frac{n}3\\right]$ global branches of nonradial solutions bifurcating from $u_1(x)=u_2(x)=U(x)=\\log\\frac{64}{(2+\\mu)\\left(8+|x|^2\\right)^2}$ at the values $\\mu=-2\\frac{n^2+n-2}{n^2+n+2}$ for any $n\\in\\mathbb N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02948","kind":"arxiv","version":3},"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"}