{"paper":{"title":"Elliptic problem involving finite many critical exponents in $\\mathbb{R}^{N}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haibo Chen, Yu Su","submitted_at":"2018-05-21T12:21:00Z","abstract_excerpt":"In this paper, we consider the following problem $$ -\\Delta u -\\zeta \\frac{u}{|x|^{2}} = \\sum_{i=1}^{k} \\left( \\int_{\\mathbb{R}^{N}} \\frac{|u|^{2^{*}_{\\alpha_{i}}}}{|x-y|^{\\alpha_{i}}} \\mathrm{d}y \\right) |u|^{2^{*}_{\\alpha_{i}}-2}u + |u|^{2^{*}-2}u , \\mathrm{~in~} \\mathbb{R}^{N}, $$ where $N\\geqslant3$, $\\zeta\\in(0,\\frac{(N-2)^{2}}{4})$, $2^{*}=\\frac{2N}{N-2}$ is the critical Sobolev exponent, and $2^{*}_{\\alpha_{i}}=\\frac{2N-\\alpha_{i}}{N-2}$ ($i=1,\\ldots,k$) are the critical Hardy--Littlewood--Sobolev upper exponents. The parameters $\\alpha_{i}$ ($i=1,\\ldots,k$) satisfy some suitable assump"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08012","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"}