{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZEMOSZIF4FT2VAXVQKBA4W6727","short_pith_number":"pith:ZEMOSZIF","schema_version":"1.0","canonical_sha256":"c918e96505e167aa82f582820e5bdfd7d32b506db02dc94132b1c36b55c04854","source":{"kind":"arxiv","id":"1807.10365","version":2},"attestation_state":"computed","paper":{"title":"Groundstate asymptotics for a class of singularly perturbed $p$-Laplacian problems in $\\mathbb {R}^N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlo Mercuri, Vitaly Moroz, Wedad Albalawi","submitted_at":"2018-07-26T21:06:29Z","abstract_excerpt":"We study the asymptotic behavior of positive groundstate solutions to the quasilinear elliptic equation \\begin{equation} -\\Delta_{p} u + \\varepsilon u^{p-1} - u^{q-1} +u^{\\mathit{l}-1} = 0 \\qquad \\text{in} \\quad \\mathbb{R}^{N}, \\end{equation} where $1<p<N $, $p<q<l<+\\infty$ and $\\varepsilon> 0 $ is a small parameter. For $\\varepsilon\\rightarrow 0$, we give a characterisation of asymptotic regimes as a function of the parameters $q$, $l$ and $N$. In particular, we show that the behavior of the groundstates is sensitive to whether $q$ is less than, equal to, or greater than the critical Sobolev "},"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":"1807.10365","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-26T21:06:29Z","cross_cats_sorted":[],"title_canon_sha256":"015c9d2c4cf6cd4a48b90a117172405ccb16b86323a79aeac69c0975b78020bf","abstract_canon_sha256":"a12b1fc5d81d2f69ba4e84da1c9e9cedbc8a8e4062afe71be650a0f783ee2796"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:30.156079Z","signature_b64":"DefKsUseggip3k1MASkBEsjrsuXuqjiilI6saWr3cvLo9UL5JfdfgdornksY85VEeQM7+L+GhcIDt77J80IqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c918e96505e167aa82f582820e5bdfd7d32b506db02dc94132b1c36b55c04854","last_reissued_at":"2026-05-17T23:46:30.155454Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:30.155454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Groundstate asymptotics for a class of singularly perturbed $p$-Laplacian problems in $\\mathbb {R}^N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlo Mercuri, Vitaly Moroz, Wedad Albalawi","submitted_at":"2018-07-26T21:06:29Z","abstract_excerpt":"We study the asymptotic behavior of positive groundstate solutions to the quasilinear elliptic equation \\begin{equation} -\\Delta_{p} u + \\varepsilon u^{p-1} - u^{q-1} +u^{\\mathit{l}-1} = 0 \\qquad \\text{in} \\quad \\mathbb{R}^{N}, \\end{equation} where $1<p<N $, $p<q<l<+\\infty$ and $\\varepsilon> 0 $ is a small parameter. For $\\varepsilon\\rightarrow 0$, we give a characterisation of asymptotic regimes as a function of the parameters $q$, $l$ and $N$. In particular, we show that the behavior of the groundstates is sensitive to whether $q$ is less than, equal to, or greater than the critical Sobolev "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10365","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":"1807.10365","created_at":"2026-05-17T23:46:30.155565+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.10365v2","created_at":"2026-05-17T23:46:30.155565+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10365","created_at":"2026-05-17T23:46:30.155565+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZEMOSZIF4FT2","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZEMOSZIF4FT2VAXV","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZEMOSZIF","created_at":"2026-05-18T12:33:07.085635+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/ZEMOSZIF4FT2VAXVQKBA4W6727","json":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727.json","graph_json":"https://pith.science/api/pith-number/ZEMOSZIF4FT2VAXVQKBA4W6727/graph.json","events_json":"https://pith.science/api/pith-number/ZEMOSZIF4FT2VAXVQKBA4W6727/events.json","paper":"https://pith.science/paper/ZEMOSZIF"},"agent_actions":{"view_html":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727","download_json":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727.json","view_paper":"https://pith.science/paper/ZEMOSZIF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.10365&json=true","fetch_graph":"https://pith.science/api/pith-number/ZEMOSZIF4FT2VAXVQKBA4W6727/graph.json","fetch_events":"https://pith.science/api/pith-number/ZEMOSZIF4FT2VAXVQKBA4W6727/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727/action/storage_attestation","attest_author":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727/action/author_attestation","sign_citation":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727/action/citation_signature","submit_replication":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727/action/replication_record"}},"created_at":"2026-05-17T23:46:30.155565+00:00","updated_at":"2026-05-17T23:46:30.155565+00:00"}