{"paper":{"title":"Fractional Hardy-Sobolev elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianfu Yang, Xiaohui Yu","submitted_at":"2015-03-01T05:07:07Z","abstract_excerpt":"In this paper, we study the following singular nonlinear elliptic problem \\begin{equation}\\label{eq:1}\n  \\left\\{\n  \\begin{array}{ll}\n  \\displaystyle (-\\Delta)^{\\frac \\alpha 2} u=\\lambda |u|^{r-2}u+\\mu\\frac{|u|^{q-2}u}{|x|^{s}}\\quad &{\\rm in }\\quad \\Omega, \\\\ \\\\ u=0 &{\\rm on }\\quad \\partial\\Omega, \\end{array} \\right.\n  \\end{equation} where $\\Omega$ is a smooth bounded domain in $\\mathbb R^N$ with $0\\in \\Omega$, $\\lambda,\\mu>0,0<s\\leq\\alpha$, $(-\\Delta)^{\\frac \\alpha 2}$ is the fractional Laplacian operator with $0<\\alpha<2$. We establish existence results of problem \\eqref{eq:1} for subcritical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00216","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"}