{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JBVYDT5XXPYKKLQ5SZCSQDTMEX","short_pith_number":"pith:JBVYDT5X","schema_version":"1.0","canonical_sha256":"486b81cfb7bbf0a52e1d9645280e6c25dec225d3722d3460e643b36ce767e41f","source":{"kind":"arxiv","id":"1802.07289","version":1},"attestation_state":"computed","paper":{"title":"Quasilinear Schr\\\"odinger-Poisson system under an exponential critical nonlinearity: existence and asymptotic of solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaetano Siciliano, Giovany M. Figueiredo","submitted_at":"2018-02-20T19:15:02Z","abstract_excerpt":"In this paper we consider the following quasilinear Schr\\\"odinger-Poisson system in a bounded domain in $\\mathbb{R}^{2}$: $$ \\left\\{ \\begin{array}[c]{ll} - \\Delta u +\\phi u = f(u) &\\ \\mbox{in } \\Omega, -\\Delta \\phi - \\varepsilon^{4}\\Delta_4 \\phi = u^{2} & \\ \\mbox{in } \\Omega, u=\\phi=0 & \\ \\mbox{on } \\partial\\Omega \\end{array}\n  \\right. $$ depending on the parameter $\\varepsilon>0$. The nonlinearity $f$ is assumed to have critical exponencial growth. We first prove existence of nontrivial solutions $(u_{\\varepsilon}, \\phi_{\\varepsilon})$ and then we show that as $\\varepsilon\\to0^{+}$ these solu"},"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":"1802.07289","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-20T19:15:02Z","cross_cats_sorted":[],"title_canon_sha256":"33634fb21095ed1e00eaaddbc0c0a583cab3fb696e221667b4d557e414e374e8","abstract_canon_sha256":"039fd8a2b5c744c63d5807c7e9a94b816ef4c957c970de22d26416163ce24b0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:50.531469Z","signature_b64":"A59ChmsV8yybh3Jw533NlppllS4ApBZYx/UgV2GZh+D9P2SYqC9c1c7CiYYNARV2OzswA4EEflcqnkO6wTnUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"486b81cfb7bbf0a52e1d9645280e6c25dec225d3722d3460e643b36ce767e41f","last_reissued_at":"2026-05-18T00:22:50.531022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:50.531022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasilinear Schr\\\"odinger-Poisson system under an exponential critical nonlinearity: existence and asymptotic of solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaetano Siciliano, Giovany M. Figueiredo","submitted_at":"2018-02-20T19:15:02Z","abstract_excerpt":"In this paper we consider the following quasilinear Schr\\\"odinger-Poisson system in a bounded domain in $\\mathbb{R}^{2}$: $$ \\left\\{ \\begin{array}[c]{ll} - \\Delta u +\\phi u = f(u) &\\ \\mbox{in } \\Omega, -\\Delta \\phi - \\varepsilon^{4}\\Delta_4 \\phi = u^{2} & \\ \\mbox{in } \\Omega, u=\\phi=0 & \\ \\mbox{on } \\partial\\Omega \\end{array}\n  \\right. $$ depending on the parameter $\\varepsilon>0$. The nonlinearity $f$ is assumed to have critical exponencial growth. We first prove existence of nontrivial solutions $(u_{\\varepsilon}, \\phi_{\\varepsilon})$ and then we show that as $\\varepsilon\\to0^{+}$ these solu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07289","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":"1802.07289","created_at":"2026-05-18T00:22:50.531090+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.07289v1","created_at":"2026-05-18T00:22:50.531090+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07289","created_at":"2026-05-18T00:22:50.531090+00:00"},{"alias_kind":"pith_short_12","alias_value":"JBVYDT5XXPYK","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"JBVYDT5XXPYKKLQ5","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"JBVYDT5X","created_at":"2026-05-18T12:32:31.084164+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/JBVYDT5XXPYKKLQ5SZCSQDTMEX","json":"https://pith.science/pith/JBVYDT5XXPYKKLQ5SZCSQDTMEX.json","graph_json":"https://pith.science/api/pith-number/JBVYDT5XXPYKKLQ5SZCSQDTMEX/graph.json","events_json":"https://pith.science/api/pith-number/JBVYDT5XXPYKKLQ5SZCSQDTMEX/events.json","paper":"https://pith.science/paper/JBVYDT5X"},"agent_actions":{"view_html":"https://pith.science/pith/JBVYDT5XXPYKKLQ5SZCSQDTMEX","download_json":"https://pith.science/pith/JBVYDT5XXPYKKLQ5SZCSQDTMEX.json","view_paper":"https://pith.science/paper/JBVYDT5X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.07289&json=true","fetch_graph":"https://pith.science/api/pith-number/JBVYDT5XXPYKKLQ5SZCSQDTMEX/graph.json","fetch_events":"https://pith.science/api/pith-number/JBVYDT5XXPYKKLQ5SZCSQDTMEX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JBVYDT5XXPYKKLQ5SZCSQDTMEX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JBVYDT5XXPYKKLQ5SZCSQDTMEX/action/storage_attestation","attest_author":"https://pith.science/pith/JBVYDT5XXPYKKLQ5SZCSQDTMEX/action/author_attestation","sign_citation":"https://pith.science/pith/JBVYDT5XXPYKKLQ5SZCSQDTMEX/action/citation_signature","submit_replication":"https://pith.science/pith/JBVYDT5XXPYKKLQ5SZCSQDTMEX/action/replication_record"}},"created_at":"2026-05-18T00:22:50.531090+00:00","updated_at":"2026-05-18T00:22:50.531090+00:00"}