{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:OBDUNZD6DQUREK2VGXMXM76M3H","short_pith_number":"pith:OBDUNZD6","schema_version":"1.0","canonical_sha256":"704746e47e1c29122b5535d9767fccd9d10bf3a157c170f84f5cdf533f9524e7","source":{"kind":"arxiv","id":"1801.08516","version":1},"attestation_state":"computed","paper":{"title":"Multiplicity of positive solutions for a quasilinear Schr\\\"odinger equation with an almost critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaetano Siciliano, Giovany M. Figueiredo, Uberlandio B. Severo","submitted_at":"2018-01-25T18:27:47Z","abstract_excerpt":"In this paper we prove an existence result of multiple positive solutions for the following quasilinear problem \\begin{equation*} \\left\\{ \\begin{array}[c]{ll} -\\Delta u - \\Delta (u^2)u = |u|^{p-2}u & \\mbox{ in } \\Omega u= 0 &\\mbox{ on } \\partial\\Omega, \\end{array} \\right. \\end{equation*} where $\\Omega$ is a smooth and bounded domain in $\\mathbb R^{N},N\\geq3$. More specifically we prove that, for $p$ near the critical exponent $22^{*}=4N/(N-2)$, the number of positive solutions is estimated below by topological invariants of the domain $\\Omega$: the Ljusternick-Schnirelmann category and the Poi"},"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":"1801.08516","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-25T18:27:47Z","cross_cats_sorted":[],"title_canon_sha256":"4b54a656a1f09bc60b5ea1b62bfb39bdfa3c4000e3c35a0fb28ee27081fd9ac0","abstract_canon_sha256":"0ce702f91df2366780afaf9d0b4172cb5ed6bbe2a8edad3d414cd35c7a83f203"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:06.140340Z","signature_b64":"O+i2b3HG7GqshW+0Mz1CkZvb3mTks3Ji5wVLE6ehxtVTZCKn3G69VfuKBDnO9UWoR9LyUEsFfJQejTlWCrBgAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"704746e47e1c29122b5535d9767fccd9d10bf3a157c170f84f5cdf533f9524e7","last_reissued_at":"2026-05-18T00:25:06.139980Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:06.139980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiplicity of positive solutions for a quasilinear Schr\\\"odinger equation with an almost critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaetano Siciliano, Giovany M. Figueiredo, Uberlandio B. Severo","submitted_at":"2018-01-25T18:27:47Z","abstract_excerpt":"In this paper we prove an existence result of multiple positive solutions for the following quasilinear problem \\begin{equation*} \\left\\{ \\begin{array}[c]{ll} -\\Delta u - \\Delta (u^2)u = |u|^{p-2}u & \\mbox{ in } \\Omega u= 0 &\\mbox{ on } \\partial\\Omega, \\end{array} \\right. \\end{equation*} where $\\Omega$ is a smooth and bounded domain in $\\mathbb R^{N},N\\geq3$. More specifically we prove that, for $p$ near the critical exponent $22^{*}=4N/(N-2)$, the number of positive solutions is estimated below by topological invariants of the domain $\\Omega$: the Ljusternick-Schnirelmann category and the Poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08516","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":"1801.08516","created_at":"2026-05-18T00:25:06.140035+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.08516v1","created_at":"2026-05-18T00:25:06.140035+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08516","created_at":"2026-05-18T00:25:06.140035+00:00"},{"alias_kind":"pith_short_12","alias_value":"OBDUNZD6DQUR","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"OBDUNZD6DQUREK2V","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"OBDUNZD6","created_at":"2026-05-18T12:32:43.782077+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/OBDUNZD6DQUREK2VGXMXM76M3H","json":"https://pith.science/pith/OBDUNZD6DQUREK2VGXMXM76M3H.json","graph_json":"https://pith.science/api/pith-number/OBDUNZD6DQUREK2VGXMXM76M3H/graph.json","events_json":"https://pith.science/api/pith-number/OBDUNZD6DQUREK2VGXMXM76M3H/events.json","paper":"https://pith.science/paper/OBDUNZD6"},"agent_actions":{"view_html":"https://pith.science/pith/OBDUNZD6DQUREK2VGXMXM76M3H","download_json":"https://pith.science/pith/OBDUNZD6DQUREK2VGXMXM76M3H.json","view_paper":"https://pith.science/paper/OBDUNZD6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.08516&json=true","fetch_graph":"https://pith.science/api/pith-number/OBDUNZD6DQUREK2VGXMXM76M3H/graph.json","fetch_events":"https://pith.science/api/pith-number/OBDUNZD6DQUREK2VGXMXM76M3H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OBDUNZD6DQUREK2VGXMXM76M3H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OBDUNZD6DQUREK2VGXMXM76M3H/action/storage_attestation","attest_author":"https://pith.science/pith/OBDUNZD6DQUREK2VGXMXM76M3H/action/author_attestation","sign_citation":"https://pith.science/pith/OBDUNZD6DQUREK2VGXMXM76M3H/action/citation_signature","submit_replication":"https://pith.science/pith/OBDUNZD6DQUREK2VGXMXM76M3H/action/replication_record"}},"created_at":"2026-05-18T00:25:06.140035+00:00","updated_at":"2026-05-18T00:25:06.140035+00:00"}