{"paper":{"title":"Classification of solutions to several semi-linear polyharmonic equations and fractional equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yuan Li, Zhenping Feng, Zhuoran Du","submitted_at":"2022-01-04T00:30:23Z","abstract_excerpt":"We are concerned with the following semi-linear polyharmonic equation with integral constraint \\begin{align} \\left\\{\\begin{array}{rl} &(-\\Delta)^pu=u^\\gamma_+ ~~ \\mbox{ in }{\\mathbb{R}^n},\\\\ \\nonumber &\\int_{\\mathbb{R}^n}u_+^{\\gamma}dx<+\\infty, \\end{array}\\right. \\end{align} where $n>2p$, $p\\geq2$ and $p\\in\\mathbb{Z}$. We obtain for $\\gamma\\in(1,\\frac{n}{n-2p})$ that any nonconstant solution satisfying certain growth at infinity is radial symmetric about some point in $\\mathbb{R}^{n}$ and monotone decreasing in the radial direction. In the case $p=2$, the same results are established for more "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.00917","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.00917/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"}