{"paper":{"title":"Nondegeneracy of positive solutions to nonlinear Hardy-Sobolev equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fr\\'ed\\'eric Robert","submitted_at":"2016-12-09T08:17:14Z","abstract_excerpt":"In this note, we prove that the kernel of the linearized equation around a positive energy solution in $\\mathbb{R}^n$, $n\\geq 3$, to $-\\Delta W-\\gamma|x|^{-2}V=|x|^{-s}W^{2^\\star(s)-1}$ is one-dimensional when $s+\\gamma>0$. Here, $s\\in [0,2)$, $0\\leq\\gamma<(n-2)^2/4$ and $2^\\star(s)=2(n-s)/(n-2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02935","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"}