{"paper":{"title":"Asymptotic behavior of positive solutions to a degenerate elliptic equation in the upper half space with a nonlinear boundary condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Zhuoran Du","submitted_at":"2015-04-16T04:07:04Z","abstract_excerpt":"We consider positive solutions of the problem \\begin{equation} \\left\\{\\begin{array}{l}-\\mbox{div}(x_{n}^{a}\\nabla u)=0\\qquad \\mbox{in}\\;\\;\\mathbb{R}_+^n,\\\\ \\frac{\\partial u}{\\partial \\nu^a}=u^{q} \\qquad \\mbox{on}\\;\\;\\partial \\mathbb{R}_+^n,\\\\ \\end{array} \\right. \\end{equation} where $a\\in (-1,0)\\cup(0,1)$, $q>1$ and $\\frac{\\partial u}{\\partial \\nu^a}:=-\\lim_{x_{n}\\rightarrow 0^+}x_{n}^{a}\\frac{\\partial u}{\\partial x_{n}}$.\n  We obtain some qualitative properties of positive axially symmetric solutions in\n  $n\\geq3$ for the case $a\\in (-1,0)$ under the condition $q\\geq\\frac{n-a}{n+a-2}$. In par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04095","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"}