{"paper":{"title":"Critical growth fractional systems with exponential nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacques Giacomoni, Konijeti Sreenadh, Pawan Kumar Mishra","submitted_at":"2015-11-11T17:12:14Z","abstract_excerpt":"We study the existence of positive solutions for the system of fractional elliptic equations of the type, \\begin{equation*} \\begin{array}{rl} (-\\Delta)^{\\frac{1}{2}} u &=\\frac{p}{p+q}\\lambda f(x)|u|^{p-2}u|v|^q + h_1(u,v) e^{u^2+v^2},\\;\\textrm{in}\\; (-1, 1),\\\\ (-\\Delta)^{\\frac{1}{2}} v &=\\frac{q}{p+q}\\lambda f(x)|u|^p|v|^{q-2}v + h_2(u,v) e^{u^2+v^2},\\;\\textrm{in}\\; (-1, 1),\n  u,v&>0 \\;\\textrm{in } \\; (-1,1),\n  u&=v=0 \\; \\text{in} \\; \\mathbb R\\setminus (-1,1).\n  \\end{array} \\end{equation*} where {$1<p+q<2$}, $h_1(u,v)=(\\alpha{+}2u^2)|u|^{\\alpha-2}u|v|^\\beta, h_2(u,v)=(\\beta{+}2v^2) |u|^\\alpha "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03579","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"}