{"paper":{"title":"Nehari Manifold for fractional Kirchhoff system with critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J. Giacomoni, J.M. do \\'O, P.K. Mishra","submitted_at":"2018-07-30T06:53:17Z","abstract_excerpt":"In this paper, we show the existence and multiplicity of positive solutions of the following fractional Kirchhoff system\\\\ \\begin{equation} \\left\\{ \\begin{array}{rllll} \\mc L_M(u)&=\\lambda f(x)|u|^{q-2}u+ \\frac{2\\alpha}{\\alpha+\\beta}\\left|u\\right|^{\\alpha-2}u|v|^\\beta & \\text{in } \\Omega,\\\\ \\mc L_M(v)&=\\mu g(x)|v|^{q-2}v+ \\frac{2\\beta}{\\alpha+\\beta}\\left|u\\right|^{\\alpha}|v|^{\\beta-2}v & \\text{in } \\Omega,\\\\ u&=v=0 &\\mbox{in } \\mathbb{R}^{N}\\setminus \\Omega, \\end{array} \\right. \\end{equation} where $\\mc L_M(u)=M\\left(\\displaystyle \\int_\\Omega|(-\\Delta)^{\\frac{s}{2}}u|^2dx\\right)(-\\Delta)^{s} u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11191","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"}