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We apply our results to equations (3) $-\\Gd_pu+a\\abs{\\nabla u}^{q}+bu^{s}=0$, (4) $\\Gd_p u+u^{-\\gamma}=0$ with $10, b\\geq 0$ and $(q-p+1)+b(s-p+1)>0$, $\\gamma>0$."},"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":"1308.2956","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-13T19:41:55Z","cross_cats_sorted":[],"title_canon_sha256":"7330e49a5d2c0da581ceb6ffed09e70e63ba3334eb864b065c8228f0e5f8eca5","abstract_canon_sha256":"09655b94d991792594574d85e8aa737785925bbdd088a68153adb07961c02555"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:18.687845Z","signature_b64":"jZq6BugP7vpL+dhxDU8/OskQ5BUmfp7ZkOrsBLBSjpl9HnBfaXuu03YWEDwwMLUf0ToAn3HMyYQmR0Z3puPLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3cf2ce99c1e10e1a5a8cc183c098f3cc5253c50a6f20da024b36039b36d9b02","last_reissued_at":"2026-05-18T02:40:18.687154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:18.687154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wiener criteria for existence of large solutions of quasilinear elliptic equations with absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hung Nguyen Quoc (LMPT), Laurent Veron (LMPT)","submitted_at":"2013-08-13T19:41:55Z","abstract_excerpt":"We obtain sufficient conditions expressed in terms of Wiener type tests involving Hausdorff or Bessel capacities for the existence of large solutions to equations (1) $-\\Gd_pu+e^{\\lambda u}+\\beta=0$ or (2) $-\\Gd_pu+\\lambda |u|^{q-1}u+\\beta=0$ in a bounded domain $\\Gw$ when $q>p-1>0, \\lambda>0$ and $\\beta\\in\\mathbb{R}$. We apply our results to equations (3) $-\\Gd_pu+a\\abs{\\nabla u}^{q}+bu^{s}=0$, (4) $\\Gd_p u+u^{-\\gamma}=0$ with $10, b\\geq 0$ and $(q-p+1)+b(s-p+1)>0$, $\\gamma>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2956","kind":"arxiv","version":4},"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":"1308.2956","created_at":"2026-05-18T02:40:18.687247+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.2956v4","created_at":"2026-05-18T02:40:18.687247+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2956","created_at":"2026-05-18T02:40:18.687247+00:00"},{"alias_kind":"pith_short_12","alias_value":"WPHSZ2M4DYIO","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"WPHSZ2M4DYIODJNI","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"WPHSZ2M4","created_at":"2026-05-18T12:28:04.890932+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/WPHSZ2M4DYIODJNIZQMDYCMPHT","json":"https://pith.science/pith/WPHSZ2M4DYIODJNIZQMDYCMPHT.json","graph_json":"https://pith.science/api/pith-number/WPHSZ2M4DYIODJNIZQMDYCMPHT/graph.json","events_json":"https://pith.science/api/pith-number/WPHSZ2M4DYIODJNIZQMDYCMPHT/events.json","paper":"https://pith.science/paper/WPHSZ2M4"},"agent_actions":{"view_html":"https://pith.science/pith/WPHSZ2M4DYIODJNIZQMDYCMPHT","download_json":"https://pith.science/pith/WPHSZ2M4DYIODJNIZQMDYCMPHT.json","view_paper":"https://pith.science/paper/WPHSZ2M4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.2956&json=true","fetch_graph":"https://pith.science/api/pith-number/WPHSZ2M4DYIODJNIZQMDYCMPHT/graph.json","fetch_events":"https://pith.science/api/pith-number/WPHSZ2M4DYIODJNIZQMDYCMPHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WPHSZ2M4DYIODJNIZQMDYCMPHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WPHSZ2M4DYIODJNIZQMDYCMPHT/action/storage_attestation","attest_author":"https://pith.science/pith/WPHSZ2M4DYIODJNIZQMDYCMPHT/action/author_attestation","sign_citation":"https://pith.science/pith/WPHSZ2M4DYIODJNIZQMDYCMPHT/action/citation_signature","submit_replication":"https://pith.science/pith/WPHSZ2M4DYIODJNIZQMDYCMPHT/action/replication_record"}},"created_at":"2026-05-18T02:40:18.687247+00:00","updated_at":"2026-05-18T02:40:18.687247+00:00"}