{"paper":{"title":"Liouville type theorem for critical order Lane-Emden-Hardy equations in $\\mathbb{R}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guolin Qin, Wei Dai, Wenxiong Chen","submitted_at":"2018-08-05T08:38:42Z","abstract_excerpt":"In this paper, we are concerned with the critical order Lane-Emden-Hardy equations \\begin{equation*}\n  (-\\Delta)^{\\frac{n}{2}}u(x)=\\frac{u^{p}(x)}{|x|^{a}} \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\text{in} \\,\\,\\, \\mathbb{R}^{n} \\end{equation*} with $n\\geq4$ is even, $0\\leq a<n$ and $1<p<+\\infty$. We prove Liouville theorem for nonnegative classical solutions to the above Lane-Emden-Hardy equations (Theorem \\ref{Thm0}), that is, the unique nonnegative solution is $u\\equiv0$. Our result seems to be the first Liouville theorem on the critical order equations in higher dimensions ($n\\geq3$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01581","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":""},"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"}