{"paper":{"title":"On singular equations with critical and supercritical exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mousomi Bhakta, Sanjiban Santra","submitted_at":"2016-08-01T16:41:38Z","abstract_excerpt":"We study the problem \\begin{equation*} (I_{\\epsilon}) \\left\\{\\begin{aligned}\n  -\\Delta u- \\frac{\\mu u}{|x|^2}&=u^p -\\epsilon u^q \\quad\\text{in }\\quad \\Omega, \\\\ u&>0 \\quad\\text{in }\\quad \\Omega, \\\\ u &\\in H^1_0(\\Omega)\\cap L^{q+1}(\\Omega),\n  \\end{aligned}\n  \\right. \\end{equation*} where $q>p\\geq 2^*-1$, $\\epsilon>0$ is a parameter, $\\Omega\\subseteq\\mathbb{R}^N$ is a bounded domain with smooth boundary, $0\\in \\Omega$, $N\\geq 3$ and $0<\\mu<\\bar\\mu:=\\big(\\frac{N-2}{2}\\big)^2$. We prove at $0$, any solution of $(I_{\\epsilon})$ has the singularity of order $|x|^{-\\nu}$ when $q<\\frac{2+\\nu}{\\nu}$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00490","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"}