{"paper":{"title":"Large number of bubble solutions for a perturbed fractional Laplacian equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Chunhua Wang, Suting Wei","submitted_at":"2019-08-09T09:42:15Z","abstract_excerpt":"This paper deals with the following nonlinear perturbed fractional Laplacian equation $$(-\\Delta)^s u = K(|y'|,y'')u^{\\frac{N+2s}{N-2s}\\pm\\epsilon},\\,\\,u>0,\\,\\,u\\in D^{1,s}(\\mathbb{R}^N),$$ where $0<s<1, N\\geq 4,$ $(y',y'')\\in \\mathbb{R}^2\\times \\mathbb{R}^{N-2},$ $\\epsilon>0$ is a small parameter and $K(y)$ is nonnegative and bounded. By combining a finite reduction argument and local Pohozaev type of identities, we prove that if $N\\geq 4,\\max\\{\\frac{N+1-\\sqrt{N^{2}-2N+9}}{4},\\frac{3-\\sqrt{N^{2}-6N+13}}{2}\\}<s<1$ and $K(r,y'')$ has a stable critical point $(r_0, y_0'')$ with $r_0>0$ and $K(r_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03386","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03386/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"}