{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:WDZP6PSUABZF2UHIEJ2HVU3FOS","short_pith_number":"pith:WDZP6PSU","schema_version":"1.0","canonical_sha256":"b0f2ff3e5400725d50e822747ad365748f7552ec0cba91815b57c3bdacc5c361","source":{"kind":"arxiv","id":"2507.12258","version":1},"attestation_state":"computed","paper":{"title":"Mixed local and nonlocal laplacian without standard critical exponent for Lane-Emden equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Quaas, Bego\\~na Barrios, Leandro M. Del Pezzo","submitted_at":"2025-07-16T14:03:15Z","abstract_excerpt":"In this paper, we investigate a mixed elliptic equation involving both local and nonlocal Laplacian operators, with a power-type nonlinearity. Specifically, we consider a Lane-Emden type equation of the form \\[-\\Delta u + (-\\Delta)^s u = u^p,\\quad\\mbox{ in }\\mathbb{R}^n.\\] where the operator combines the classical Laplacian and the fractional Laplacian. We establish the existence of solutions for exponents slightly below the critical local Sobolev exponent, that is, for $p < \\frac{n+2}{n-2}$, with $p$ close to $\\frac{n+2}{n-2}$.\n  Our results show that, due to the interaction between the local"},"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":"2507.12258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-16T14:03:15Z","cross_cats_sorted":[],"title_canon_sha256":"1d44b8bedda5d50bf547033bec5051bf98f4a78122c1ed400df7be5b7e0c384f","abstract_canon_sha256":"e99407687544a3898ffad380301fdfda4b56e12fb2e29761e9aa13a343f9f89d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:17.501719Z","signature_b64":"jPVdiw8oTwECIixORpVzl8ud9LpeKlqfE/E/xkv7GSkZ3iXaoYdjnqhC4fMAPV2osaAFvzrNIWmgKownqJ7WDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0f2ff3e5400725d50e822747ad365748f7552ec0cba91815b57c3bdacc5c361","last_reissued_at":"2026-07-05T11:38:17.501199Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:17.501199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mixed local and nonlocal laplacian without standard critical exponent for Lane-Emden equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Quaas, Bego\\~na Barrios, Leandro M. Del Pezzo","submitted_at":"2025-07-16T14:03:15Z","abstract_excerpt":"In this paper, we investigate a mixed elliptic equation involving both local and nonlocal Laplacian operators, with a power-type nonlinearity. Specifically, we consider a Lane-Emden type equation of the form \\[-\\Delta u + (-\\Delta)^s u = u^p,\\quad\\mbox{ in }\\mathbb{R}^n.\\] where the operator combines the classical Laplacian and the fractional Laplacian. We establish the existence of solutions for exponents slightly below the critical local Sobolev exponent, that is, for $p < \\frac{n+2}{n-2}$, with $p$ close to $\\frac{n+2}{n-2}$.\n  Our results show that, due to the interaction between the local"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12258","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.12258/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2507.12258","created_at":"2026-07-05T11:38:17.501258+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.12258v1","created_at":"2026-07-05T11:38:17.501258+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12258","created_at":"2026-07-05T11:38:17.501258+00:00"},{"alias_kind":"pith_short_12","alias_value":"WDZP6PSUABZF","created_at":"2026-07-05T11:38:17.501258+00:00"},{"alias_kind":"pith_short_16","alias_value":"WDZP6PSUABZF2UHI","created_at":"2026-07-05T11:38:17.501258+00:00"},{"alias_kind":"pith_short_8","alias_value":"WDZP6PSU","created_at":"2026-07-05T11:38:17.501258+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/WDZP6PSUABZF2UHIEJ2HVU3FOS","json":"https://pith.science/pith/WDZP6PSUABZF2UHIEJ2HVU3FOS.json","graph_json":"https://pith.science/api/pith-number/WDZP6PSUABZF2UHIEJ2HVU3FOS/graph.json","events_json":"https://pith.science/api/pith-number/WDZP6PSUABZF2UHIEJ2HVU3FOS/events.json","paper":"https://pith.science/paper/WDZP6PSU"},"agent_actions":{"view_html":"https://pith.science/pith/WDZP6PSUABZF2UHIEJ2HVU3FOS","download_json":"https://pith.science/pith/WDZP6PSUABZF2UHIEJ2HVU3FOS.json","view_paper":"https://pith.science/paper/WDZP6PSU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.12258&json=true","fetch_graph":"https://pith.science/api/pith-number/WDZP6PSUABZF2UHIEJ2HVU3FOS/graph.json","fetch_events":"https://pith.science/api/pith-number/WDZP6PSUABZF2UHIEJ2HVU3FOS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WDZP6PSUABZF2UHIEJ2HVU3FOS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WDZP6PSUABZF2UHIEJ2HVU3FOS/action/storage_attestation","attest_author":"https://pith.science/pith/WDZP6PSUABZF2UHIEJ2HVU3FOS/action/author_attestation","sign_citation":"https://pith.science/pith/WDZP6PSUABZF2UHIEJ2HVU3FOS/action/citation_signature","submit_replication":"https://pith.science/pith/WDZP6PSUABZF2UHIEJ2HVU3FOS/action/replication_record"}},"created_at":"2026-07-05T11:38:17.501258+00:00","updated_at":"2026-07-05T11:38:17.501258+00:00"}