{"paper":{"title":"Classification of solutions to equations involving Higher-order fractional Laplacian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiaqi Hu, Yuan Li, Zhenping Feng, Zhuoran Du","submitted_at":"2022-02-03T04:56:34Z","abstract_excerpt":"In this paper, we are concerned with the following equation involving higher-order fractional Lapalacian \\begin{equation*} \\left\\{\\begin{aligned} &(-\\Delta)^{p+{\\frac{\\alpha}{2}}}u(x)=u_+^\\gamma~~ \\mbox{ in }\\mathbb{R}^n,\\\\ &\\int_{\\mathbb{R}^n}u_+^\\gamma dx<+\\infty, \\end{aligned}\\right. \\end{equation*} where $p\\geq 1$ is an integer, $0<\\alp<2$, $n> 2p+\\alpha$ and $\\gamma \\in (1,\\frac{n}{n-2p-\\alp})$. We establish an integral representation formula for any nonconstant classical solution satisfying certain growth at infinity. From this we prove that these solutions are radially symmetric about s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.01409","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/2202.01409/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"}