{"paper":{"title":"Large singular solutions for conformal $Q$-curvature equations on $\\mathbb{S}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hui Yang, Xusheng Du","submitted_at":"2020-09-04T08:45:57Z","abstract_excerpt":"In this paper, we study the existence of positive functions $K \\in C^1(\\mathbb{S}^n)$ such that the conformal $Q$-curvature equation \\begin{equation}\\label{001} P_m (v) =K v^{\\frac{n+2m}{n-2m}}~~~~~~ {on} ~ \\mathbb{S}^n \\{equation} has a singular positive solution $v$ whose singular set is a single point, where $m$ is an integer satisfying $1 \\leq m < n/2$ and $P_m$ is the intertwining operator of order $2m$. More specifically, we show that when $n\\geq 2m+4$, every positive function in $C^1(\\mathbb{S}^n)$ can be approximated in the $C^1(\\mathbb{S}^n)$ norm by a positive function $K\\in C^1(\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.02069","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.02069/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}