{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:YAAJOUFJHTPL6SZTQX2XKMETD4","short_pith_number":"pith:YAAJOUFJ","schema_version":"1.0","canonical_sha256":"c0009750a93cdebf4b3385f57530931f155497d8769cd64164540e2f496bd260","source":{"kind":"arxiv","id":"1908.11247","version":2},"attestation_state":"computed","paper":{"title":"On a class of weighted p-Laplace equation with singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"P. Garain, T. Mukherjee","submitted_at":"2019-08-29T14:13:37Z","abstract_excerpt":"This article deals with the existence of the following quasilinear degenerate singular elliptic equation \\begin{equation*} (P_\\la)\\left\\{ \\begin{split}\n  -\\text{div}(w(x)|\\nabla u|^{p-2}\\nabla u) &= g_{\\la}(u),\\;u>0\\; \\text{in}\\; \\Om,\n  u&=0 \\; \\text{on}\\; \\partial \\Om, \\end{split}\\right. \\end{equation*} where $ \\Om \\subset \\mb R^n$ is a smooth bounded domain, $n\\geq 3$, $\\la>0$, $p>1$ and $w$ is a Muckenhoupt weight. Using variational techniques, for $g_{\\la}(u)= \\la f(u)u^{-q}$ and certain assumptions on $f$, we show existence of a solution to $(P_\\la)$ for each $\\la>0$. Moreover when $g_{\\l"},"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":"1908.11247","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-29T14:13:37Z","cross_cats_sorted":[],"title_canon_sha256":"ebbc8ef5baea1ba090c1759bd35f18fdced98f3bd164f1d6f2a890e5c6f26035","abstract_canon_sha256":"35dc072741fab1076a9cba3a8ec4ab0defd3eb997412a0016cc3c172391894da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:26:10.035373Z","signature_b64":"n2z45yl0h1YDQG4V1jvpT0EbCOtZO6o7oGXSutdWAaLDwcs9qq8lUP2OZAuAqWV2BhOP84DQg3Zg0VfyZlzJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0009750a93cdebf4b3385f57530931f155497d8769cd64164540e2f496bd260","last_reissued_at":"2026-07-05T00:26:10.034882Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:26:10.034882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a class of weighted p-Laplace equation with singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"P. Garain, T. Mukherjee","submitted_at":"2019-08-29T14:13:37Z","abstract_excerpt":"This article deals with the existence of the following quasilinear degenerate singular elliptic equation \\begin{equation*} (P_\\la)\\left\\{ \\begin{split}\n  -\\text{div}(w(x)|\\nabla u|^{p-2}\\nabla u) &= g_{\\la}(u),\\;u>0\\; \\text{in}\\; \\Om,\n  u&=0 \\; \\text{on}\\; \\partial \\Om, \\end{split}\\right. \\end{equation*} where $ \\Om \\subset \\mb R^n$ is a smooth bounded domain, $n\\geq 3$, $\\la>0$, $p>1$ and $w$ is a Muckenhoupt weight. Using variational techniques, for $g_{\\la}(u)= \\la f(u)u^{-q}$ and certain assumptions on $f$, we show existence of a solution to $(P_\\la)$ for each $\\la>0$. Moreover when $g_{\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.11247","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.11247/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.11247","created_at":"2026-07-05T00:26:10.034945+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.11247v2","created_at":"2026-07-05T00:26:10.034945+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.11247","created_at":"2026-07-05T00:26:10.034945+00:00"},{"alias_kind":"pith_short_12","alias_value":"YAAJOUFJHTPL","created_at":"2026-07-05T00:26:10.034945+00:00"},{"alias_kind":"pith_short_16","alias_value":"YAAJOUFJHTPL6SZT","created_at":"2026-07-05T00:26:10.034945+00:00"},{"alias_kind":"pith_short_8","alias_value":"YAAJOUFJ","created_at":"2026-07-05T00:26:10.034945+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/YAAJOUFJHTPL6SZTQX2XKMETD4","json":"https://pith.science/pith/YAAJOUFJHTPL6SZTQX2XKMETD4.json","graph_json":"https://pith.science/api/pith-number/YAAJOUFJHTPL6SZTQX2XKMETD4/graph.json","events_json":"https://pith.science/api/pith-number/YAAJOUFJHTPL6SZTQX2XKMETD4/events.json","paper":"https://pith.science/paper/YAAJOUFJ"},"agent_actions":{"view_html":"https://pith.science/pith/YAAJOUFJHTPL6SZTQX2XKMETD4","download_json":"https://pith.science/pith/YAAJOUFJHTPL6SZTQX2XKMETD4.json","view_paper":"https://pith.science/paper/YAAJOUFJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.11247&json=true","fetch_graph":"https://pith.science/api/pith-number/YAAJOUFJHTPL6SZTQX2XKMETD4/graph.json","fetch_events":"https://pith.science/api/pith-number/YAAJOUFJHTPL6SZTQX2XKMETD4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YAAJOUFJHTPL6SZTQX2XKMETD4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YAAJOUFJHTPL6SZTQX2XKMETD4/action/storage_attestation","attest_author":"https://pith.science/pith/YAAJOUFJHTPL6SZTQX2XKMETD4/action/author_attestation","sign_citation":"https://pith.science/pith/YAAJOUFJHTPL6SZTQX2XKMETD4/action/citation_signature","submit_replication":"https://pith.science/pith/YAAJOUFJHTPL6SZTQX2XKMETD4/action/replication_record"}},"created_at":"2026-07-05T00:26:10.034945+00:00","updated_at":"2026-07-05T00:26:10.034945+00:00"}