{"paper":{"title":"Solutions for fractional operator problem via local Pohozaev identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianjun Nie, Ting Liu, Yuxia Guo","submitted_at":"2019-04-17T15:26:33Z","abstract_excerpt":"We consider the following fractional Schr\\\"{o}dinger equation involving critical exponent: \\begin{equation*} \\left\\{\\begin{array}{ll} (-\\Delta)^s u+V(|y'|,y'')u=u^{2^*_s-1} \\ \\hbox{ in } \\ \\mathbb{R}^N, \\\\ u>0, \\ y \\in \\mathbb{R}^N, \\end{array}\\right. \\end{equation*} where $s\\in(\\frac{1}{2}, 1)$, $(y',y'')\\in \\mathbb{R}^2\\times \\mathbb{R}^{N-2}$, $V(|y'|,y'')$ is a bounded nonnegative function with a weaker symmetry condition. We prove the existence of infinitely many solutions for the above problem by a finite dimensional reduction method combining various Pohazaev identies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08316","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"}