{"paper":{"title":"Existence and phase separation of entire solutions to a pure critical competitive elliptic system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, M\\'onica Clapp","submitted_at":"2017-08-31T13:31:34Z","abstract_excerpt":"We establish the existence of a positive fully nontrivial solution $(u,v)$ to the weakly coupled elliptic system% \\[ \\left\\{ \\begin{tabular} [c]{l}% $-\\Delta u=\\mu_{1}|u|^{{2}^{\\ast}-2}u+\\lambda\\alpha|u|^{\\alpha-2}|v|^{\\beta }u,$\\\\ $-\\Delta v=\\mu_{2}|v|^{{2}^{\\ast}-2}v+\\lambda\\beta|u|^{\\alpha}|v|^{\\beta{-2}% }v,$\\\\ $u,v\\in D^{1,2}(\\mathbb{R}^{N}),$% \\end{tabular} \\ \\right. \\] where $N\\geq4,$ $2^{\\ast}:=\\frac{2N}{N-2}$ is the critical Sobolev exponent, $\\alpha,\\beta\\in(1,2],$ $\\alpha+\\beta=2^{\\ast},$ $\\mu_{1},\\mu_{2}>0,$ and $\\lambda<0.$ We show that these solutions exhibit phase separation as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09701","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"}