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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","authors_text":"Jing Zeng, Liang-Gen Hu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2015-02-14T01:15:02Z","title":"Liouville type theorems for stable solutions of the weighted elliptic system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04157","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:59e899a1e07bbd021241a93b8db4c14c412a5667222c151a97f2b868070a0379","target":"record","created_at":"2026-05-18T02:25:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"71f9f12316765ccadda86d8f809286c6a3ab10e5321a6cf66ea8c857474cab83","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2015-02-14T01:15:02Z","title_canon_sha256":"a727429120e1b8b5af9687722232f957f9409aae47ab074f52581ad20fc9275e"},"schema_version":"1.0","source":{"id":"1502.04157","kind":"arxiv","version":2}},"canonical_sha256":"512acd26c15e02f602f0bbf3e2e2780823f6b80d349c38cd5aaa07a39facb350","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"512acd26c15e02f602f0bbf3e2e2780823f6b80d349c38cd5aaa07a39facb350","first_computed_at":"2026-05-18T02:25:55.479967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:55.479967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NO+bylzktJcHYZm8vBjX0YE3cS3jAki3xpZyXwxDAzvf3+EAIb1+wArQJPvukmCqgbf3+RHDjVqr+M3fkmWpBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:55.480407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04157","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59e899a1e07bbd021241a93b8db4c14c412a5667222c151a97f2b868070a0379","sha256:f7197fd316eceb0aba1fdaa53d141ceb8da31321cc88d7f76d0dc4a6baca9c45"],"state_sha256":"25c3a80b9d44962c81618d87375860afeaf89517db3deac2c109cd1109c66d97"}