{"paper":{"title":"A perturbed nonlinear elliptic PDE with two Hardy-Sobolev critical 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":"2015-04-03T02:42:03Z","abstract_excerpt":"Let $\\Omega$ be a $C^1$ open bounded domain in $\\R^N$ ($N\\geq 3$) with $0\\in \\partial \\Omega$. Suppose that $\\partial\\Omega$ is $C^2$ at $0$ and the mean curvature of $\\partial\\Omega$ at $0$ is negative. Consider the following perturbed PDE involving two Hardy-Sobolev critical exponents: $$ \\begin{cases} &\\Delta u+\\lambda_1 \\frac{u^{2^*(s_1)-1}}{|x|^{s_1}}+\\lambda_2\\frac{u^{2^*(s_2)-1}}{|x|^{s_2}}+\\lambda_3\\frac{u^p}{|x|^{s_3}}=0\\;\\quad \\hbox{in}\\;\\Omega,\\\\ &u(x)>0\\;\\hbox{in}\\;\\Omega,\\;\\, u(x)=0\\;\\hbox{on}\\;\\partial\\Omega, \\end{cases} $$ where $0<s_2<s_1<2, 0\\leq s_3<2, 2^*(s_i):=\\frac{2(N-s_i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00730","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"}