{"paper":{"title":"Isolated singularities of positive solutions for Choquard equations in sublinear case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feng Zhou, Huyuan Chen","submitted_at":"2016-10-28T02:45:40Z","abstract_excerpt":"Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case $q \\in (0,1)$\n  $$\\displaystyle \\ \\ -\\Delta u+ u =I_\\alpha[u^p] u^q\\;\\;\n  {\\rm in}\\; \\mathbb{R}^N\\setminus\\{0\\},\n  % [2mm] \\phantom{ }\n  \\;\\; \\displaystyle \\lim_{|x|\\to+\\infty}u(x)=0, $$ where $p >0, N \\geq 3, \\alpha \\in (0,N)$ and $I_{\\alpha}[u^p](x) = \\int_{\\mathbb{R}^N} \\frac{u^p(y)}{|x-y|^{N-\\alpha}}dy$ is the Riesz potential, which appears as a nonlocal term in the equation. We investigate the nonexistence and existence of isolated singular solutions of Choquar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09062","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":""},"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"}