{"paper":{"title":"On isolated singularities of Kirchhoff--type Laplacian problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Binlin Zhang, Huyuan Chen, Mouhamed Moustapha Fall","submitted_at":"2017-08-10T00:44:07Z","abstract_excerpt":"In this paper, we study isolated singular positive solutions for the following Kirchhoff--type Laplacian problem: \\begin{equation*} -\\left(\\theta+\\int_{\\Omega} |\\nabla u| dx\\right)\\Delta u =u^p \\quad{\\rm in}\\quad \\Omega\\setminus \\{0\\},\\qquad u=0\\quad {\\rm on}\\quad \\partial \\Omega, \\end{equation*} where $p>1$, $\\theta\\in \\R$, $\\Omega$ is a bounded smooth domain containing the origin in $\\R^N$ with $N\\ge 2$. In the subcritical case: $1<p<N/(N-2)$ if $N\\ge3$, $1<p<+\\infty$ if $N=2$, we employ the Schauder fixed-point theorem to derive a sequence of positive isolated singular solutions for the abo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03041","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"}