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In this equation, the exponent p satisfies either p > 1 when n:=m-k \\leq 2 or p\\in (1, \\frac{n+2}{n-2}) when n>2. In particular p c"},"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":"1210.1705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-10-05T10:50:07Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"45dd788c1380a696a516e58a1c4ee38091625a114dc394a3615660da7c369b55","abstract_canon_sha256":"f01b126404fe96ee2f503f3ba8ae8170396053d9a10d973d5f75ba9df7675aca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:53.546680Z","signature_b64":"FMtY2mylO/L9Ffoj1pNkFrGB4fLLTv+K9tuu7E/hfbZtC1WPpECiWV8EN53ZsxviNVKMnTuIqntpEkcTQ/xqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d97e157cc399975e87389ba895d541394c44bc08c3c434ed2b9ef12f48202a8","last_reissued_at":"2026-05-18T03:43:53.546022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:53.546022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solutions of semilinear elliptic equations in tubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Berardino Sciunzi, Filomena Pacella, Frank Pacard","submitted_at":"2012-10-05T10:50:07Z","abstract_excerpt":"Given a smooth compact k-dimensional manifold \\Lambda embedded in $\\mathbb {R}^m$, with m\\geq 2 and 1\\leq k\\leq m-1, and given \\epsilon>0, we define B_\\epsilon (\\Lambda) to be the geodesic tubular neighborhood of radius \\epsilon about \\Lambda.\n  In this paper, we construct positive solutions of the semilinear elliptic equation \\Delta u + u^p = 0 in B_\\epsilon (\\Lambda) with u = 0 on \\partial B_\\epsilon (\\Lambda), when the parameter \\epsilon is chosen small enough. In this equation, the exponent p satisfies either p > 1 when n:=m-k \\leq 2 or p\\in (1, \\frac{n+2}{n-2}) when n>2. 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