{"paper":{"title":"Semilinear fractional elliptic equations with measures in unbounded domain","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huyuan Chen, Jianfu Yang","submitted_at":"2014-03-06T19:03:20Z","abstract_excerpt":"In this paper, we study the existence of nonnegative weak solutions to (E) $ (-\\Delta)^\\alpha u+h(u)=\\nu $ in a general regular domain $\\Omega$, which vanish in $\\R^N\\setminus\\Omega$, where $(-\\Delta)^\\alpha$ denotes the fractional Laplacian with $\\alpha\\in(0,1)$, $\\nu$ is a nonnegative Radon measure and $h:\\mathbb{R}_+\\to\\mathbb{R}_+$ is a continuous nondecreasing function satisfying a subcritical integrability condition. Furthermore, we analyze properties of weak solution $u_k$ to $(E)$ with $\\Omega=\\mathbb{R}^N$, $\\nu=k\\delta_0$ and $h(s)=s^p$, where $k>0$, $p\\in(0,\\frac{N}{N-2\\alpha})$ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1530","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"}