{"paper":{"title":"Non-existence of stable solutions for weighted $p$-Laplace equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kaushik Bal, Prashanta Garain","submitted_at":"2017-09-16T11:15:33Z","abstract_excerpt":"We provide sufficient conditions on $w\\in L^1_{loc}(\\mathbb{R}^N)$ such that the weighted $p$-Laplace equation $$-\\operatorname{div}\\big(w(x)|\\nabla u|^{p-2}\\nabla u\\big)=f(u)\\;\\;\\mbox{in}\\;\\;\\mathbb{R}^N$$ does not admit any stable $C^{1,\\zeta}_{loc}$ solution in $\\mathbb{R}^N$ where $f(x)$ is either $-x^{-\\delta}$ or $e^x$ for any $0<\\zeta<1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05497","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"}