{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7IZ2M7GPRDM42HGEE6KO64MWVI","short_pith_number":"pith:7IZ2M7GP","schema_version":"1.0","canonical_sha256":"fa33a67ccf88d9cd1cc42794ef7196aa29c18324e9c1eac3bbb6161707e11690","source":{"kind":"arxiv","id":"1307.2757","version":1},"attestation_state":"computed","paper":{"title":"Semilinear elliptic equations admitting similarity transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Moshe Marcus, Mousomi Bhakta","submitted_at":"2013-07-10T11:28:17Z","abstract_excerpt":"In this paper we study the equation $-\\Delta u+\\rho^{-(\\alpha+2)}h(\\rho^{\\alpha}u)=0$ in a smooth bounded domain $\\Omega$ where $\\rho(x)=\\textrm{dist}\\,(x,\\partial \\Omega)$, $\\alpha>0$ and $h$ is a non-decreasing function which satisfies Keller-Osserman condition. We introduce a condition on $h$ which implies that the equation is subcritical, i.e. the corresponding boundary value problem is well posed with respect to data given by finite measures. Under additional assumptions on $h$ we show that this condition is necessary as well as sufficient. We also discuss b.v. problems with data given by"},"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":"1307.2757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-10T11:28:17Z","cross_cats_sorted":[],"title_canon_sha256":"be1887607f5221b3df2f2601187d49250a525c0297537703278541a1769d3fd0","abstract_canon_sha256":"7efaffae1cecba6370b80524b9c7f3585c6b619f0dd4de275add0e28234823a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:10.845947Z","signature_b64":"ZKAAdN1E9WiQWhUviyCppObA7qUDO8w6Uabp2+9NcUpEM8bV6oE+yM9QpHVEm69ykUPNdSUjR71lGWzMerOaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa33a67ccf88d9cd1cc42794ef7196aa29c18324e9c1eac3bbb6161707e11690","last_reissued_at":"2026-05-18T02:20:10.845242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:10.845242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semilinear elliptic equations admitting similarity transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Moshe Marcus, Mousomi Bhakta","submitted_at":"2013-07-10T11:28:17Z","abstract_excerpt":"In this paper we study the equation $-\\Delta u+\\rho^{-(\\alpha+2)}h(\\rho^{\\alpha}u)=0$ in a smooth bounded domain $\\Omega$ where $\\rho(x)=\\textrm{dist}\\,(x,\\partial \\Omega)$, $\\alpha>0$ and $h$ is a non-decreasing function which satisfies Keller-Osserman condition. We introduce a condition on $h$ which implies that the equation is subcritical, i.e. the corresponding boundary value problem is well posed with respect to data given by finite measures. Under additional assumptions on $h$ we show that this condition is necessary as well as sufficient. We also discuss b.v. problems with data given by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2757","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":"1307.2757","created_at":"2026-05-18T02:20:10.845361+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.2757v1","created_at":"2026-05-18T02:20:10.845361+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2757","created_at":"2026-05-18T02:20:10.845361+00:00"},{"alias_kind":"pith_short_12","alias_value":"7IZ2M7GPRDM4","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7IZ2M7GPRDM42HGE","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7IZ2M7GP","created_at":"2026-05-18T12:27:36.564083+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/7IZ2M7GPRDM42HGEE6KO64MWVI","json":"https://pith.science/pith/7IZ2M7GPRDM42HGEE6KO64MWVI.json","graph_json":"https://pith.science/api/pith-number/7IZ2M7GPRDM42HGEE6KO64MWVI/graph.json","events_json":"https://pith.science/api/pith-number/7IZ2M7GPRDM42HGEE6KO64MWVI/events.json","paper":"https://pith.science/paper/7IZ2M7GP"},"agent_actions":{"view_html":"https://pith.science/pith/7IZ2M7GPRDM42HGEE6KO64MWVI","download_json":"https://pith.science/pith/7IZ2M7GPRDM42HGEE6KO64MWVI.json","view_paper":"https://pith.science/paper/7IZ2M7GP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.2757&json=true","fetch_graph":"https://pith.science/api/pith-number/7IZ2M7GPRDM42HGEE6KO64MWVI/graph.json","fetch_events":"https://pith.science/api/pith-number/7IZ2M7GPRDM42HGEE6KO64MWVI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7IZ2M7GPRDM42HGEE6KO64MWVI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7IZ2M7GPRDM42HGEE6KO64MWVI/action/storage_attestation","attest_author":"https://pith.science/pith/7IZ2M7GPRDM42HGEE6KO64MWVI/action/author_attestation","sign_citation":"https://pith.science/pith/7IZ2M7GPRDM42HGEE6KO64MWVI/action/citation_signature","submit_replication":"https://pith.science/pith/7IZ2M7GPRDM42HGEE6KO64MWVI/action/replication_record"}},"created_at":"2026-05-18T02:20:10.845361+00:00","updated_at":"2026-05-18T02:20:10.845361+00:00"}