{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AHDCXZKW6ZZVPWJTQBGJWNBXB4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d279cc980d50ed7e0d415f9af6b1a1736ff64a268b98321430389afe8bd4b462","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-11T04:57:59Z","title_canon_sha256":"2172edceff1d296542642515e33a9311c5b99f41ebd0b2dffd34a67a89e75478"},"schema_version":"1.0","source":{"id":"1804.03812","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03812","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03812v1","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03812","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"pith_short_12","alias_value":"AHDCXZKW6ZZV","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AHDCXZKW6ZZVPWJT","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AHDCXZKW","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:a23a92448be8f683786a74c9a2e6fb426dc22c0d1d24f4b89a78570c1be46717","target":"graph","created_at":"2026-05-18T00:18:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we prove the existence of multiple nontrivial solutions of the following equation. \\begin{align*} \\begin{split} -\\Delta_{p}u & = \\lambda |u|^{q-2}u+f(x,u)+\\mu\\,\\,\\mbox{in}\\,\\,\\Omega, u & = 0\\,\\, \\mbox{on}\\,\\, \\partial\\Omega; \\end{split} \\end{align*} where $\\Omega \\subset \\mathbb{R}^N$ is a smooth bounded domain with $N \\geq 3$, $1 < q^{\\prime} < q < p-1; \\; \\lambda,\\;$ and $f$ satisfies certain conditions, $\\mu>0$ is a Radon measure, $q^{\\prime}=\\frac{q}{q-1}$ is the conjugate of $q$.","authors_text":"Amita Soni, D. Choudhuri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-11T04:57:59Z","title":"Existence of multiple solutions to an elliptic problem with measure data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03812","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:41990422cfc1c90a985b29f2390888cfe0ec314d422dd37a8a0ddde95fabf164","target":"record","created_at":"2026-05-18T00:18:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d279cc980d50ed7e0d415f9af6b1a1736ff64a268b98321430389afe8bd4b462","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-11T04:57:59Z","title_canon_sha256":"2172edceff1d296542642515e33a9311c5b99f41ebd0b2dffd34a67a89e75478"},"schema_version":"1.0","source":{"id":"1804.03812","kind":"arxiv","version":1}},"canonical_sha256":"01c62be556f67357d933804c9b34370f2b36278a8b1fce17acee18bbe2277423","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01c62be556f67357d933804c9b34370f2b36278a8b1fce17acee18bbe2277423","first_computed_at":"2026-05-18T00:18:42.989094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:42.989094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yK1zA++I3sevYED/RVYpGjq3eSzLH7BYmciCroqN3uowhk3X44f2WFBbg7SareNFbiNZZhM9AXoLBKj+rm08BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:42.989739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03812","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41990422cfc1c90a985b29f2390888cfe0ec314d422dd37a8a0ddde95fabf164","sha256:a23a92448be8f683786a74c9a2e6fb426dc22c0d1d24f4b89a78570c1be46717"],"state_sha256":"9dae0559457f2b07585f842c2b2f0ccf28a688ab13635d7f78fa001db4a28c61"}