{"paper":{"title":"Symmetry and Nonexistence of Positive Solutions for Fractional Choquard Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jihui Zhang, Pei Ma","submitted_at":"2017-04-07T11:26:43Z","abstract_excerpt":"This paper is devoted to study the following Choquard equation \\begin{eqnarray*}\\left\\{ \\begin{array}{lll}\n  (-\\triangle)^{\\alpha/2}u=(|x|^{\\beta-n}\\ast u^p)u^{p-1},~~~&x\\in R^n, u\\geq0,\\,\\,&x\\in R^n,\n  \\end{array}\n  \\right. \\end{eqnarray*} where $0<\\alpha,\\beta<2$, $1\\leq p<\\infty$, and $n\\geq2$. Using a direct method of moving planes, we prove the symmetry and nonexistence of positive solutions in the critical and subcritical case respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02190","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"}