{"paper":{"title":"Liouville type theorems for stable solutions of the weighted elliptic system","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jing Zeng, Liang-Gen Hu","submitted_at":"2015-02-14T01:15:02Z","abstract_excerpt":"We examine the weighted elliptic system \\begin{equation*} \\begin{cases} -\\Delta u=(1+|x|^2)^{\\frac{\\alpha}{2}} v,\\\\ -\\Delta v=(1+|x|^2)^{\\frac{\\alpha}{2}} u^p, \\end{cases} \\quad \\mbox{in}\\;\\ \\mathbb{R}^N, \\end{equation*}where $N \\ge 5$, $p>1$ and $\\alpha >0$. We prove Liouville type results for the classical positive (nonnegative) stable solutions in dimension $N<\\ell+\\dfrac{\\alpha (\\ell-2)}{2}$ ($N <\\ell+\\dfrac{\\alpha (\\ell-2)(p+3)}{4(p+1)}$) and $\\ell \\ge 5$, $p \\in (1,p_*(\\ell))$. In particular, for any $p>1$ and $\\alpha > 0$, we obtain the nonexistence of classical positive (nonnegative) s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04157","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"}