{"paper":{"title":"On Elliptic Systems involving critical Hardy-Sobolev exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenming Zou, Xuexiu Zhong","submitted_at":"2015-04-04T10:54:39Z","abstract_excerpt":"Let $\\Omega\\subset \\R^N$ ($N\\geq 3$) be an open domain which is not necessarily bounded. By using variational methods, we consider the following elliptic systems involving multiple Hardy-Sobolev critical exponents: $$\\begin{cases} -\\Delta u-\\lambda \\frac{|u|^{2^*(s_1)-2}u}{|x|^{s_1}}=\\kappa\\alpha \\frac{1}{|x|^{s_2}}|u|^{\\alpha-2}u|v|^\\beta\\quad &\\hbox{in}\\;\\Omega,\\\\ -\\Delta v-\\mu \\frac{|v|^{2^*(s_1)-2}v}{|x|^{s_1}}=\\kappa\\beta \\frac{1}{|x|^{s_2}}|u|^{\\alpha}|v|^{\\beta-2}v\\quad &\\hbox{in}\\;\\Omega,\\\\ (u,v)\\in \\mathscr{D}:=D_{0}^{1,2}(\\Omega)\\times D_{0}^{1,2}(\\Omega), \\end{cases}$$ where $s_1,s_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01005","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"}