{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:F5ACFYPOLFUURBAFPBF7XLCPU4","short_pith_number":"pith:F5ACFYPO","schema_version":"1.0","canonical_sha256":"2f4022e1ee5969488405784bfbac4fa726cbec1825cb66766f80ee2d72871e9f","source":{"kind":"arxiv","id":"1407.6931","version":2},"attestation_state":"computed","paper":{"title":"Existence, uniqueness and qualitative properties of positive solutions of quasilinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hoang-Hung Vo, Phuoc-Tai Nguyen","submitted_at":"2014-07-25T15:13:11Z","abstract_excerpt":"We study the following quasilinear elliptic equation $$ -\\Delta_p u + (\\beta\\Phi(x)-a(x)) u^{p-1} + b(x)g(u)=0 \\quad \\text{in } \\mathbb{R}^N \\quad \\quad \\quad (P_\\beta) $$ where $p>1$, $\\Phi \\in L^\\infty_{loc}(\\mathbb{R}^N)$, $a,b \\in L^\\infty(\\mathbb{R}^N)$, $\\beta,b,g \\geq 0$. We provide a sharp criterion in terms of generalized principal eigenvalue for existence/nonexistence of positive solutions of ($P_\\beta$) in suitable classes of functions. We derive the uniqueness result of ($P_\\beta$) in those classes. Under additional conditions on $\\Phi$, we further show that :\n  i) either for every"},"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":"1407.6931","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-25T15:13:11Z","cross_cats_sorted":[],"title_canon_sha256":"5938f576de4db740411df51ead36f64e338d90f111da635c262342fbf3b665bf","abstract_canon_sha256":"ccf35e2ed9d5265b5e199e747564ff06854fb41c7c0abdb860131802f9c573be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:16.893175Z","signature_b64":"/qVRXyLHPsVp3GdEOBd8EWrZtV11AXXJ4ySDYuNmgzDBa3UQhoHaeiaT2tJZyOcsQvcbQlIg/JSs+jAbkLD6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f4022e1ee5969488405784bfbac4fa726cbec1825cb66766f80ee2d72871e9f","last_reissued_at":"2026-05-18T01:32:16.892431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:16.892431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence, uniqueness and qualitative properties of positive solutions of quasilinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hoang-Hung Vo, Phuoc-Tai Nguyen","submitted_at":"2014-07-25T15:13:11Z","abstract_excerpt":"We study the following quasilinear elliptic equation $$ -\\Delta_p u + (\\beta\\Phi(x)-a(x)) u^{p-1} + b(x)g(u)=0 \\quad \\text{in } \\mathbb{R}^N \\quad \\quad \\quad (P_\\beta) $$ where $p>1$, $\\Phi \\in L^\\infty_{loc}(\\mathbb{R}^N)$, $a,b \\in L^\\infty(\\mathbb{R}^N)$, $\\beta,b,g \\geq 0$. We provide a sharp criterion in terms of generalized principal eigenvalue for existence/nonexistence of positive solutions of ($P_\\beta$) in suitable classes of functions. We derive the uniqueness result of ($P_\\beta$) in those classes. Under additional conditions on $\\Phi$, we further show that :\n  i) either for every"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6931","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":""},"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":"1407.6931","created_at":"2026-05-18T01:32:16.892513+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.6931v2","created_at":"2026-05-18T01:32:16.892513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6931","created_at":"2026-05-18T01:32:16.892513+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5ACFYPOLFUU","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5ACFYPOLFUURBAF","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5ACFYPO","created_at":"2026-05-18T12:28:28.263976+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/F5ACFYPOLFUURBAFPBF7XLCPU4","json":"https://pith.science/pith/F5ACFYPOLFUURBAFPBF7XLCPU4.json","graph_json":"https://pith.science/api/pith-number/F5ACFYPOLFUURBAFPBF7XLCPU4/graph.json","events_json":"https://pith.science/api/pith-number/F5ACFYPOLFUURBAFPBF7XLCPU4/events.json","paper":"https://pith.science/paper/F5ACFYPO"},"agent_actions":{"view_html":"https://pith.science/pith/F5ACFYPOLFUURBAFPBF7XLCPU4","download_json":"https://pith.science/pith/F5ACFYPOLFUURBAFPBF7XLCPU4.json","view_paper":"https://pith.science/paper/F5ACFYPO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.6931&json=true","fetch_graph":"https://pith.science/api/pith-number/F5ACFYPOLFUURBAFPBF7XLCPU4/graph.json","fetch_events":"https://pith.science/api/pith-number/F5ACFYPOLFUURBAFPBF7XLCPU4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5ACFYPOLFUURBAFPBF7XLCPU4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5ACFYPOLFUURBAFPBF7XLCPU4/action/storage_attestation","attest_author":"https://pith.science/pith/F5ACFYPOLFUURBAFPBF7XLCPU4/action/author_attestation","sign_citation":"https://pith.science/pith/F5ACFYPOLFUURBAFPBF7XLCPU4/action/citation_signature","submit_replication":"https://pith.science/pith/F5ACFYPOLFUURBAFPBF7XLCPU4/action/replication_record"}},"created_at":"2026-05-18T01:32:16.892513+00:00","updated_at":"2026-05-18T01:32:16.892513+00:00"}