{"paper":{"title":"On a class of semilinear fractional elliptic equations involving outside Dirac data","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hichem Hajaiej, Huyuan Chen, Ying Wang","submitted_at":"2015-01-26T02:52:10Z","abstract_excerpt":"The purpose of this article is to give a complete study of the weak solutions of the fractional elliptic equation \\begin{equation}\\label{00}\n  \\arraycolsep=1pt \\begin{array}{lll}\n  (-\\Delta)^{\\alpha} u+u^p=0\\ \\ \\ \\ &\\ {\\rm in}\\ \\ B_1(e_N),\\\\[2mm]\\phantom{(-\\Delta)^{\\alpha} +u^p}\n  u=\\delta_{0}& \\ {\\rm in}\\ \\ \\mathbb{R}^N\\setminus B_1(e_N), \\end{array} \\end{equation} where $p>0$, $ (-\\Delta)^{\\alpha}$ with $\\alpha\\in(0,1)$ denotes the fractional Laplacian operator in the principle value sense, $B_1(e_N)$ is the unit ball\n  centered at $e_N=(0,\\cdots,0,1)$ in $\\mathbb{R}^N$ with $N\\ge 2$ and $\\d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06242","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"}