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We provide a complete characterization of the set of $(p,\\sigma)\\in\\R^2$ such that the equation has no positive (super-)solutions, depending on the values of $A,B$ and the principle Dirichlet eigenvalue of the cross--section of the cone.\n  The proofs are based on the explicit construction of appropriate barriers an"},"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":"math/0501025","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2005-01-02T19:58:17Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"2fdf20cca84b0ec0d71bf2e8a8274fa946b768963345a3b57d25ff666ebee073","abstract_canon_sha256":"9653e1339442799dc12f191f81c4a3559d3193bc003656cd7b00879b3c6292e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:31.816524Z","signature_b64":"kCOVOPc4wIctvZXUs7Eoskm2HiLsYmkoG+bW9SbfQ6XRKQTZWizCeug5x3QQzgzZznxIwr5aspmorPblslECDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"560a54071908593bff0ab9f0407acd9a3f42d0a6dd2bd66df36452d8d7054a2d","last_reissued_at":"2026-05-18T00:09:31.815988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:31.815988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positive solutions to singular semilinear elliptic equations with critical potential on cone-like domains","license":"","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Sofya Lyakhova, Vitali Liskevich, Vitaly Moroz","submitted_at":"2005-01-02T19:58:17Z","abstract_excerpt":"We study the existence and nonexistence of positive (super-)solutions to a singular semilinear elliptic equation $$-\\nabla\\cdot(|x|^A\\nabla u)-B|x|^{A-2}u=C|x|^{A-\\sigma}u^p$$ in cone--like domains of $\\R^N$ ($N\\ge 2$), for the full range of parameters $A,B,\\sigma,p\\in\\R$ and $C>0$. We provide a complete characterization of the set of $(p,\\sigma)\\in\\R^2$ such that the equation has no positive (super-)solutions, depending on the values of $A,B$ and the principle Dirichlet eigenvalue of the cross--section of the cone.\n  The proofs are based on the explicit construction of appropriate barriers an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501025","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0501025","created_at":"2026-05-18T00:09:31.816075+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0501025v1","created_at":"2026-05-18T00:09:31.816075+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501025","created_at":"2026-05-18T00:09:31.816075+00:00"},{"alias_kind":"pith_short_12","alias_value":"KYFFIBYZBBMT","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"KYFFIBYZBBMTX7YK","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"KYFFIBYZ","created_at":"2026-05-18T12:25:53.335082+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KYFFIBYZBBMTX7YKXHYEA6WNTI","json":"https://pith.science/pith/KYFFIBYZBBMTX7YKXHYEA6WNTI.json","graph_json":"https://pith.science/api/pith-number/KYFFIBYZBBMTX7YKXHYEA6WNTI/graph.json","events_json":"https://pith.science/api/pith-number/KYFFIBYZBBMTX7YKXHYEA6WNTI/events.json","paper":"https://pith.science/paper/KYFFIBYZ"},"agent_actions":{"view_html":"https://pith.science/pith/KYFFIBYZBBMTX7YKXHYEA6WNTI","download_json":"https://pith.science/pith/KYFFIBYZBBMTX7YKXHYEA6WNTI.json","view_paper":"https://pith.science/paper/KYFFIBYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0501025&json=true","fetch_graph":"https://pith.science/api/pith-number/KYFFIBYZBBMTX7YKXHYEA6WNTI/graph.json","fetch_events":"https://pith.science/api/pith-number/KYFFIBYZBBMTX7YKXHYEA6WNTI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KYFFIBYZBBMTX7YKXHYEA6WNTI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KYFFIBYZBBMTX7YKXHYEA6WNTI/action/storage_attestation","attest_author":"https://pith.science/pith/KYFFIBYZBBMTX7YKXHYEA6WNTI/action/author_attestation","sign_citation":"https://pith.science/pith/KYFFIBYZBBMTX7YKXHYEA6WNTI/action/citation_signature","submit_replication":"https://pith.science/pith/KYFFIBYZBBMTX7YKXHYEA6WNTI/action/replication_record"}},"created_at":"2026-05-18T00:09:31.816075+00:00","updated_at":"2026-05-18T00:09:31.816075+00:00"}