{"paper":{"title":"On a critical Kirchhoff problem in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yisheng Huang, Yuanze Wu, Zeng Liu","submitted_at":"2016-05-23T06:41:57Z","abstract_excerpt":"In this paper, we consider the following Kirchhoff problem $$ \\left\\{\\aligned -\\bigg(a+b\\int_{\\Omega}|\\nabla u|^2dx\\bigg)\\Delta u&= \\lambda u^{q-1} + \\mu u^{2^*-1}, &\\quad \\text{in }\\Omega, \\\\ u&>0,&\\quad\\text{in }\\Omega,\\\\ u&=0,&\\quad\\text{on }\\partial\\Omega, \\endaligned \\right.\\eqno{(\\mathcal{P})} $$ where $\\Omega\\subset \\bbr^N(N\\geq4)$ is a bounded domain, $2\\leq q<2^*$, $2^*=\\frac{2N}{N-2}$ is the critical Sobolev exponent and $a$, $b$, $\\lambda$, $\\mu$ are positive parameters. By using the variational method, we obtain some existence and nonexistence results to $(\\mathcal{P})$ for all $N\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06906","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"}