{"paper":{"title":"Liouville theorems for stable solutions of the weighted Lane-Emden system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdellaziz Harrabi, Foued Mtiri, Hatem Hajlaoui","submitted_at":"2015-11-20T19:51:05Z","abstract_excerpt":"We examine the general weighted Lane-Emden system \\begin{align*}\n  -\\Delta u = \\rho(x)v^p,\\quad -\\Delta v= \\rho(x)u^\\theta, \\quad u,v>0\\quad \\mbox{in }\\;\\mathbb{R}^N \\end{align*}\n  where $1<p\\leq\\theta$ and\n  $\\rho: \\mathbb{R}^N\\rightarrow \\mathbb{R}$ is a radial continuous function satisfying\n  $\\rho(x)\\geq A(1+|x|^2)^{\\frac{\\alpha}{2}}$ in $\\mathbb{R}^N$ for some $\\alpha\\geq 0$ and $A>0$. We\n  prove some Liouville type results for stable solution and improve the previous works \\cite{co, Fa, HU}. In particular, we establish a new comparison property\n  (see Proposition 1.1 below) which is cruc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06736","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"}