{"paper":{"title":"Uniqueness and nondegeneracy of positive solutions of $\\Ds u+u=u^p$ in $\\R^N$ when $s$ is close to 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Mouhamed Moustapha Fall","submitted_at":"2013-01-21T14:03:35Z","abstract_excerpt":"We consider the equation $\\Ds u+u=u^p$, with $s\\in(0,1)$ in the subcritical range of $p$. We prove that if $s$ is sufficiently close to 1 the equation possesses a unique minimizer, which is nondegenerate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4868","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"}