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Our argument is based on a nonexistence result of positive supersolution of a linear elliptic problem with Hardy potential. We also est"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.02531","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-03-07T05:50:12Z","cross_cats_sorted":[],"title_canon_sha256":"9d1b0de00336f04e3a01711e6241bd522ad164e21ed06972934901d7829ef278","abstract_canon_sha256":"0d837a89e1af6701b3711010e26d8043f0285802ff53cd12555f637167a35a94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:54.179686Z","signature_b64":"arR2OQVXVqPSVcIZTzQQc/uNoEc47W0Dk1mhR+O0GNDghGpVjcVRNa9tCDCwSVotCFVW0lOz9N7GGL0fmE9qCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcbad64d3ae0a12a0e01baa4e893cce1f51e165f9a8d5d4b49f484e85f4d14cc","last_reissued_at":"2026-05-17T23:57:54.178990Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:54.178990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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