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We prove Liouville theorems for nonnegative classical solutions to the above Lane-Emden-Hardy equations (Theorem \\ref{Thm0}), that is, the unique nonnegative solution is $u\\equiv0$. As an application, we derive a priori estimates and existen"},"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":"1808.10771","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-30T13:51:19Z","cross_cats_sorted":[],"title_canon_sha256":"432ae5f5a4017e6104a0fd2f416b3caf4bab561c97f6847237a13f7fe9f64051","abstract_canon_sha256":"cd35128d55bb50ed9a5402e1d33294e4583dea8f8dce70de18de03f525b91859"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:20.045731Z","signature_b64":"/kqnSFUJb87EjodsPmylr0/vKF+J2tQ7x3Stb98QR4PcSyC+v+7NAScID3IIbX1srLn52C665tp2rhYqjEl0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec14df1f8f74227618bc54a6e3bf6f4e59a40b16c9610fe2db28a1c8a3be61d6","last_reissued_at":"2026-05-18T00:04:20.045077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:20.045077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Liouville type theorems, a priori estimates and existence of solutions for non-critical higher order Lane-Emden-Hardy equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guolin Qin, Shaolong Peng, Wei Dai","submitted_at":"2018-08-30T13:51:19Z","abstract_excerpt":"In this paper, we are concerned with the non-critical higher order Lane-Emden-Hardy equations \\begin{equation*}\n  (-\\Delta)^{m}u(x)=\\frac{u^{p}(x)}{|x|^{a}} \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\text{in} \\,\\,\\, \\mathbb{R}^{n} \\end{equation*} with $n\\geq3$, $1\\leq m<\\frac{n}{2}$, $0\\leq a<2m$, $1<p<\\frac{n+2m-2a}{n-2m}$ if $0\\leq a<2$, and $1<p<\\infty$ if $2\\leq a<2m$. We prove Liouville theorems for nonnegative classical solutions to the above Lane-Emden-Hardy equations (Theorem \\ref{Thm0}), that is, the unique nonnegative solution is $u\\equiv0$. 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