{"paper":{"title":"Elliptic equations involving general subcritical source nonlinearity and measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huyuan Chen, Laurent V\\'eron, Patricio Felmer","submitted_at":"2014-09-10T13:46:06Z","abstract_excerpt":"In this article, we study the existence of positive solutions to elliptic equation (E1) $$(-\\Delta)^\\alpha u=g(u)+\\sigma\\nu \\quad{\\rm in}\\quad \\Omega,$$ subject to the condition (E2) $$u=\\varrho\\mu\\quad {\\rm on}\\quad \\partial\\Omega\\ \\ {\\rm if}\\ \\alpha=1\\qquad {\\rm or\\ \\ in}\\ \\ \\Omega^c \\ \\ {\\rm if}\\ \\alpha\\in(0,1),$$\n  where $\\sigma,\\varrho\\ge0$, $\\Omega$ is an open bounded $C^2$ domain in $\\mathbb{R}^N$, $(-\\Delta)^\\alpha$ denotes the fractional Laplacian with $\\alpha\\in(0,1)$ or Laplacian operator if $\\alpha=1$, $\\nu,\\mu$ are suitable Radon measures\n  and $g:\\mathbb{R}_+\\mapsto\\mathbb{R}_+$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3067","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"}