{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KEVM2JWBLYBPMAXQXPZ6FYTYBA","short_pith_number":"pith:KEVM2JWB","schema_version":"1.0","canonical_sha256":"512acd26c15e02f602f0bbf3e2e2780823f6b80d349c38cd5aaa07a39facb350","source":{"kind":"arxiv","id":"1502.04157","version":2},"attestation_state":"computed","paper":{"title":"Liouville type theorems for stable solutions of the weighted elliptic system","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jing Zeng, Liang-Gen Hu","submitted_at":"2015-02-14T01:15:02Z","abstract_excerpt":"We examine the weighted elliptic system \\begin{equation*} \\begin{cases} -\\Delta u=(1+|x|^2)^{\\frac{\\alpha}{2}} v,\\\\ -\\Delta v=(1+|x|^2)^{\\frac{\\alpha}{2}} u^p, \\end{cases} \\quad \\mbox{in}\\;\\ \\mathbb{R}^N, \\end{equation*}where $N \\ge 5$, $p>1$ and $\\alpha >0$. We prove Liouville type results for the classical positive (nonnegative) stable solutions in dimension $N<\\ell+\\dfrac{\\alpha (\\ell-2)}{2}$ ($N <\\ell+\\dfrac{\\alpha (\\ell-2)(p+3)}{4(p+1)}$) and $\\ell \\ge 5$, $p \\in (1,p_*(\\ell))$. In particular, for any $p>1$ and $\\alpha > 0$, we obtain the nonexistence of classical positive (nonnegative) s"},"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":"1502.04157","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2015-02-14T01:15:02Z","cross_cats_sorted":[],"title_canon_sha256":"a727429120e1b8b5af9687722232f957f9409aae47ab074f52581ad20fc9275e","abstract_canon_sha256":"71f9f12316765ccadda86d8f809286c6a3ab10e5321a6cf66ea8c857474cab83"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:55.480407Z","signature_b64":"NO+bylzktJcHYZm8vBjX0YE3cS3jAki3xpZyXwxDAzvf3+EAIb1+wArQJPvukmCqgbf3+RHDjVqr+M3fkmWpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"512acd26c15e02f602f0bbf3e2e2780823f6b80d349c38cd5aaa07a39facb350","last_reissued_at":"2026-05-18T02:25:55.479967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:55.479967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Liouville type theorems for stable solutions of the weighted elliptic system","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jing Zeng, Liang-Gen Hu","submitted_at":"2015-02-14T01:15:02Z","abstract_excerpt":"We examine the weighted elliptic system \\begin{equation*} \\begin{cases} -\\Delta u=(1+|x|^2)^{\\frac{\\alpha}{2}} v,\\\\ -\\Delta v=(1+|x|^2)^{\\frac{\\alpha}{2}} u^p, \\end{cases} \\quad \\mbox{in}\\;\\ \\mathbb{R}^N, \\end{equation*}where $N \\ge 5$, $p>1$ and $\\alpha >0$. We prove Liouville type results for the classical positive (nonnegative) stable solutions in dimension $N<\\ell+\\dfrac{\\alpha (\\ell-2)}{2}$ ($N <\\ell+\\dfrac{\\alpha (\\ell-2)(p+3)}{4(p+1)}$) and $\\ell \\ge 5$, $p \\in (1,p_*(\\ell))$. In particular, for any $p>1$ and $\\alpha > 0$, we obtain the nonexistence of classical positive (nonnegative) s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04157","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":"1502.04157","created_at":"2026-05-18T02:25:55.480035+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.04157v2","created_at":"2026-05-18T02:25:55.480035+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04157","created_at":"2026-05-18T02:25:55.480035+00:00"},{"alias_kind":"pith_short_12","alias_value":"KEVM2JWBLYBP","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"KEVM2JWBLYBPMAXQ","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"KEVM2JWB","created_at":"2026-05-18T12:29:27.538025+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/KEVM2JWBLYBPMAXQXPZ6FYTYBA","json":"https://pith.science/pith/KEVM2JWBLYBPMAXQXPZ6FYTYBA.json","graph_json":"https://pith.science/api/pith-number/KEVM2JWBLYBPMAXQXPZ6FYTYBA/graph.json","events_json":"https://pith.science/api/pith-number/KEVM2JWBLYBPMAXQXPZ6FYTYBA/events.json","paper":"https://pith.science/paper/KEVM2JWB"},"agent_actions":{"view_html":"https://pith.science/pith/KEVM2JWBLYBPMAXQXPZ6FYTYBA","download_json":"https://pith.science/pith/KEVM2JWBLYBPMAXQXPZ6FYTYBA.json","view_paper":"https://pith.science/paper/KEVM2JWB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.04157&json=true","fetch_graph":"https://pith.science/api/pith-number/KEVM2JWBLYBPMAXQXPZ6FYTYBA/graph.json","fetch_events":"https://pith.science/api/pith-number/KEVM2JWBLYBPMAXQXPZ6FYTYBA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KEVM2JWBLYBPMAXQXPZ6FYTYBA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KEVM2JWBLYBPMAXQXPZ6FYTYBA/action/storage_attestation","attest_author":"https://pith.science/pith/KEVM2JWBLYBPMAXQXPZ6FYTYBA/action/author_attestation","sign_citation":"https://pith.science/pith/KEVM2JWBLYBPMAXQXPZ6FYTYBA/action/citation_signature","submit_replication":"https://pith.science/pith/KEVM2JWBLYBPMAXQXPZ6FYTYBA/action/replication_record"}},"created_at":"2026-05-18T02:25:55.480035+00:00","updated_at":"2026-05-18T02:25:55.480035+00:00"}