{"paper":{"title":"Qualitative properties of positive solutions of quasilinear equations with Hardy terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yutian Lei","submitted_at":"2013-05-05T10:35:53Z","abstract_excerpt":"In this paper, we are concerned with the quasilinear PDE with weight $$ -div A(x,\\nabla u)=|x|^a u^q(x), \\quad u>0 \\quad \\textrm{in} \\quad R^n, $$ where $n \\geq 3$, $q>p-1$ with $p \\in (1,2]$ and $a \\in (-n,0]$. The positive weak solution $u$ of the quasilinear PDE is $\\mathcal{A}$-superharmonic and satisfies $\\inf_{R^n}u=0$. We can introduce an integral equation involving the wolff potential $$ u(x)=R(x) W_{\\beta,p}(|y|^au^q(y))(x), \\quad u>0 \\quad \\textrm{in} \\quad R^n, $$ which the positive solution $u$ of the quasilinear PDE satisfies. Here $p \\in (1,2]$, $q>p-1$, $\\beta>0$ and $0 \\leq -a<"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1003","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"}