{"paper":{"title":"Nonexistence of Positive Supersolution to a Class of Semilinear Elliptic Equations and Systems in an Exterior Domain","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feng Zhou, Huyuan Chen, Rui Peng","submitted_at":"2018-03-07T05:50:12Z","abstract_excerpt":"In this paper, we primarily consider the following semilinear elliptic equation\n  \\begin{eqnarray*}\n  \\arraycolsep=1pt\\left\\{\n  \\begin{array}{lll}\n  \\displaystyle -\\Delta u= h(x,u)\\quad \\\n  &{\\rm in}\\ \\Omega,\\\\[1.5mm]\n  \\phantom{ -\\Delta }\n  \\displaystyle u\\ge 0\\qquad &{\\rm on}\\ \\partial{\\Omega},\n  \\end{array}\\right.\n  \\end{eqnarray*} where $\\Omega$ is an exterior domain in $R^N$ with $N\\ge 3$, and derive optimal nonexistence results of positive supersolution. Our argument is based on a nonexistence result of positive supersolution of a linear elliptic problem with Hardy potential. We also est"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02531","kind":"arxiv","version":3},"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"}