{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:46WSSH4A5TJW7AGW635ZXLAR3Q","short_pith_number":"pith:46WSSH4A","schema_version":"1.0","canonical_sha256":"e7ad291f80ecd36f80d6f6fb9bac11dc1afe8aafcd7a5dcbd662c122b1ff7868","source":{"kind":"arxiv","id":"1606.01370","version":1},"attestation_state":"computed","paper":{"title":"Elliptic Problems in $\\mathbb{R}^N$ with Critical and Singular Discontinuous Nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K. Sreenadh, R. Dhanya, S. Prashanth, Sweta Tiwari","submitted_at":"2016-06-04T11:26:05Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in $\\mathbb R^{N}$, $N\\geq3$ with smooth boundary,\n  $a>0, \\lambda>0$ and $0<\\delta<3$ be real numbers. Define $2^*:=\\displaystyle\\frac{2N}{N-2}$ and the characteristic function of a set $A$ by $\\chi_A$.\n  We consider the following critical problem with singular and discontinuous nonlinearity: \\begin{eqnarray*}\n  (P_\\la^a)~~~~ \\qquad \\Biggl\\{\\begin{array}{rl} -\\Delta u &= \\lambda \\left(u^{2^*-1}+ \\displaystyle \\chi_{\\{u<a\\}}u^{-\\de} \\right), u > 0~~\\text{in} ~~\\Omega, \\\\ u & = 0 ~\\text{on}~\n  \\partial \\Omega. \\end{array} \\end{eqnarray*}\n  \\noindent We study the"},"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":"1606.01370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-04T11:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"b86028996b38dcda2a2da0e6b79984947fe72766debef09b74b2deb736ad5846","abstract_canon_sha256":"3c7551420f9ddc21f62f145c5c740a5be0c1358ebf1cc388376765de138f0313"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:54.309493Z","signature_b64":"dcWvpN10OZ8lO+JNMd/q15zL68tN+DZwB1MfzUepTC0y7DMlwywhfjBA0RioRRG/3zo/gfvw+ToJiBEfW3ZaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7ad291f80ecd36f80d6f6fb9bac11dc1afe8aafcd7a5dcbd662c122b1ff7868","last_reissued_at":"2026-05-18T01:12:54.308988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:54.308988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elliptic Problems in $\\mathbb{R}^N$ with Critical and Singular Discontinuous Nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K. Sreenadh, R. Dhanya, S. Prashanth, Sweta Tiwari","submitted_at":"2016-06-04T11:26:05Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in $\\mathbb R^{N}$, $N\\geq3$ with smooth boundary,\n  $a>0, \\lambda>0$ and $0<\\delta<3$ be real numbers. Define $2^*:=\\displaystyle\\frac{2N}{N-2}$ and the characteristic function of a set $A$ by $\\chi_A$.\n  We consider the following critical problem with singular and discontinuous nonlinearity: \\begin{eqnarray*}\n  (P_\\la^a)~~~~ \\qquad \\Biggl\\{\\begin{array}{rl} -\\Delta u &= \\lambda \\left(u^{2^*-1}+ \\displaystyle \\chi_{\\{u<a\\}}u^{-\\de} \\right), u > 0~~\\text{in} ~~\\Omega, \\\\ u & = 0 ~\\text{on}~\n  \\partial \\Omega. \\end{array} \\end{eqnarray*}\n  \\noindent We study the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01370","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":"1606.01370","created_at":"2026-05-18T01:12:54.309074+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.01370v1","created_at":"2026-05-18T01:12:54.309074+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01370","created_at":"2026-05-18T01:12:54.309074+00:00"},{"alias_kind":"pith_short_12","alias_value":"46WSSH4A5TJW","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"46WSSH4A5TJW7AGW","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"46WSSH4A","created_at":"2026-05-18T12:29:58.707656+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/46WSSH4A5TJW7AGW635ZXLAR3Q","json":"https://pith.science/pith/46WSSH4A5TJW7AGW635ZXLAR3Q.json","graph_json":"https://pith.science/api/pith-number/46WSSH4A5TJW7AGW635ZXLAR3Q/graph.json","events_json":"https://pith.science/api/pith-number/46WSSH4A5TJW7AGW635ZXLAR3Q/events.json","paper":"https://pith.science/paper/46WSSH4A"},"agent_actions":{"view_html":"https://pith.science/pith/46WSSH4A5TJW7AGW635ZXLAR3Q","download_json":"https://pith.science/pith/46WSSH4A5TJW7AGW635ZXLAR3Q.json","view_paper":"https://pith.science/paper/46WSSH4A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.01370&json=true","fetch_graph":"https://pith.science/api/pith-number/46WSSH4A5TJW7AGW635ZXLAR3Q/graph.json","fetch_events":"https://pith.science/api/pith-number/46WSSH4A5TJW7AGW635ZXLAR3Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/46WSSH4A5TJW7AGW635ZXLAR3Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/46WSSH4A5TJW7AGW635ZXLAR3Q/action/storage_attestation","attest_author":"https://pith.science/pith/46WSSH4A5TJW7AGW635ZXLAR3Q/action/author_attestation","sign_citation":"https://pith.science/pith/46WSSH4A5TJW7AGW635ZXLAR3Q/action/citation_signature","submit_replication":"https://pith.science/pith/46WSSH4A5TJW7AGW635ZXLAR3Q/action/replication_record"}},"created_at":"2026-05-18T01:12:54.309074+00:00","updated_at":"2026-05-18T01:12:54.309074+00:00"}