{"paper":{"title":"Liouville Type Theorem for Some Nonlocal Elliptic Equations","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xiaohui Yu","submitted_at":"2017-06-12T05:03:38Z","abstract_excerpt":"In this paper, we prove some Liouville theorem for the following elliptic equations involving nonlocal nonlinearity and nonlocal boundary value condition $$ \\left\\{\n  \\begin{array}{ll}\n  \\displaystyle -\\Delta u(y)=\\intpr \\frac{ F(u(x',0))}{|(x',0)-y|^{N-\\alpha}}dx'g(u(y)), &y\\in\\R, \\\\ \\\\ \\displaystyle\n  \\frac{\\partial u}{\\partial \\nu}(x',0)=\\intr \\frac{G(u(y))}{|(x',0)-y|^{N-\\alpha}}\\,dy f(u(x',0)), &(x',0)\\in\\partial \\mathbb R_+^N, \\end{array} \\right. $$ where $\\mathbb R_+^N=\\{x\\in \\mathbb R^N:x_N>0\\}$, $f,g,F,G$ are some nonlinear functions. Under some assumptions on the nonlinear functions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03467","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"}