{"paper":{"title":"A perturbative approach to non-degeneracy of the Lane-Emden system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Seunghyeok Kim","submitted_at":"2019-07-25T20:46:38Z","abstract_excerpt":"We consider ground state solutions of the critical Lane-Emden system \\[\\begin{cases} -\\Delta u = v^p &\\text{in } \\mathbb{R}^n,\\\\ -\\Delta v = u^q &\\text{in } \\mathbb{R}^n,\\\\ u,v >0\\ &\\text{in } \\mathbb{R}^n, \\end{cases}\\] where $n \\ge 3$ and $p,q>0$ and $(p,q)$ belongs to the critical hyperbola $\\frac{1}{p+1} + \\frac{1}{q+1} = \\frac{n-2}{n}.$ We prove that they are non-degenerate when either $(p,q)$ is close to $(1,{n+4\\over n-4})$ (if $n\\ge5$) or $(p,q)$ is close to $({n+2\\over n-2},{n+2\\over n-2})$ (if $n\\ge3$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11303","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"}