{"paper":{"title":"Uniqueness of nonnegative weak solution to $u^p\\le(-\\Delta)^\\frac{\\alpha}{2}u$ on $\\mathbb R^N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jie Xiao, Yuzhao Wang","submitted_at":"2015-01-20T15:14:21Z","abstract_excerpt":"This note shows that under $(p,\\alpha, N)\\in (1,\\infty)\\times(0,2)\\times\\mathbb Z_+$ the fractional order differential inequality $$ (\\dagger)\\quad u^p \\le (-\\Delta)^{\\frac{\\alpha}{2}} u\\quad\\hbox{in}\\quad\\mathbb R^{N} $$ has the property that if $N\\le\\alpha$ then a nonnegative solution to $(\\dagger)$ is unique, and if $N>\\alpha$ then the uniqueness of a nonnegative weak solution to $(\\dagger)$ occurs when and only when $p\\le N/(N-\\alpha)$, thereby innovatively generalizing Gidas-Spruck's result for $u^p+\\Delta u\\le 0$ in $\\R^N$ discovered in \\cite{GS}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04842","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"}