{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FCA4CSTXHH6NJ36JONDR5XN4YH","short_pith_number":"pith:FCA4CSTX","schema_version":"1.0","canonical_sha256":"2881c14a7739fcd4efc973471eddbcc1c19f1655ab02ad26d8b4b31fe2b82c05","source":{"kind":"arxiv","id":"1106.4622","version":1},"attestation_state":"computed","paper":{"title":"Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yunyan Yang","submitted_at":"2011-06-23T04:30:21Z","abstract_excerpt":"In this paper a quasi-linear elliptic equation in the whole Euclidean space is considered. The nonlinearity of the equation is assumed to have exponential growth or have critical growth in view of Trudinger-Moser type inequality. Under some assumptions on the potential and the nonlinearity, it is proved that there is a nontrivial positive weak solution to this equation. Also it is shown that there are two distinct positive weak solutions to a perturbation of the equation. The method of proving these results is combining Trudinger-Moser type inequality, Mountain-pass theorem and Ekeland's varia"},"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":"1106.4622","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2011-06-23T04:30:21Z","cross_cats_sorted":[],"title_canon_sha256":"5d74ac0e1c2ee6dd80f733e899e5bf1307f876dc94bcafd5ed74d9226be8079d","abstract_canon_sha256":"0255db30188f5baba875fd308799fca26876849b49dc73ce763a619b70d31ae2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:31.830410Z","signature_b64":"4jXiI+AsmFuvYcPhI56NCpQSaU3mTGYeBWq5kz07T9wu2lxY6RIQRBZRwKLnXvIrrd/kbV+Ii4HFjIC832mSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2881c14a7739fcd4efc973471eddbcc1c19f1655ab02ad26d8b4b31fe2b82c05","last_reissued_at":"2026-05-18T04:19:31.830038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:31.830038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yunyan Yang","submitted_at":"2011-06-23T04:30:21Z","abstract_excerpt":"In this paper a quasi-linear elliptic equation in the whole Euclidean space is considered. The nonlinearity of the equation is assumed to have exponential growth or have critical growth in view of Trudinger-Moser type inequality. Under some assumptions on the potential and the nonlinearity, it is proved that there is a nontrivial positive weak solution to this equation. Also it is shown that there are two distinct positive weak solutions to a perturbation of the equation. The method of proving these results is combining Trudinger-Moser type inequality, Mountain-pass theorem and Ekeland's varia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4622","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":"1106.4622","created_at":"2026-05-18T04:19:31.830089+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.4622v1","created_at":"2026-05-18T04:19:31.830089+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4622","created_at":"2026-05-18T04:19:31.830089+00:00"},{"alias_kind":"pith_short_12","alias_value":"FCA4CSTXHH6N","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FCA4CSTXHH6NJ36J","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FCA4CSTX","created_at":"2026-05-18T12:26:28.662955+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/FCA4CSTXHH6NJ36JONDR5XN4YH","json":"https://pith.science/pith/FCA4CSTXHH6NJ36JONDR5XN4YH.json","graph_json":"https://pith.science/api/pith-number/FCA4CSTXHH6NJ36JONDR5XN4YH/graph.json","events_json":"https://pith.science/api/pith-number/FCA4CSTXHH6NJ36JONDR5XN4YH/events.json","paper":"https://pith.science/paper/FCA4CSTX"},"agent_actions":{"view_html":"https://pith.science/pith/FCA4CSTXHH6NJ36JONDR5XN4YH","download_json":"https://pith.science/pith/FCA4CSTXHH6NJ36JONDR5XN4YH.json","view_paper":"https://pith.science/paper/FCA4CSTX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.4622&json=true","fetch_graph":"https://pith.science/api/pith-number/FCA4CSTXHH6NJ36JONDR5XN4YH/graph.json","fetch_events":"https://pith.science/api/pith-number/FCA4CSTXHH6NJ36JONDR5XN4YH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FCA4CSTXHH6NJ36JONDR5XN4YH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FCA4CSTXHH6NJ36JONDR5XN4YH/action/storage_attestation","attest_author":"https://pith.science/pith/FCA4CSTXHH6NJ36JONDR5XN4YH/action/author_attestation","sign_citation":"https://pith.science/pith/FCA4CSTXHH6NJ36JONDR5XN4YH/action/citation_signature","submit_replication":"https://pith.science/pith/FCA4CSTXHH6NJ36JONDR5XN4YH/action/replication_record"}},"created_at":"2026-05-18T04:19:31.830089+00:00","updated_at":"2026-05-18T04:19:31.830089+00:00"}