{"paper":{"title":"Blowup analysis for integral equations on bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qianqiao Guo","submitted_at":"2018-08-27T08:03:05Z","abstract_excerpt":"Consider the integral equation \\begin{equation*} f^{q-1}(x)=\\int_\\Omega\\frac{f(y)}{|x-y|^{n-\\alpha}}dy,\\ \\ f(x)>0,\\quad x\\in \\overline \\Omega, \\end{equation*} where $\\Omega\\subset \\mathbb{R}^n$ is a smooth bounded domain. For $1<\\alpha<n$, the existence of energy maximizing positive solution in subcritical case $2<q<\\frac{2n}{n+\\alpha}$, and nonexistence of energy maximizing positive solution in critical case $q=\\frac{2n}{n+\\alpha}$ are proved in \\cite{DZ2017}. For $\\alpha>n$, the existence of energy minimizing positive solution in subcritical case $0<q<\\frac{2n}{n+\\alpha}$, and nonexistence o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08723","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"}