{"paper":{"title":"Asymptotic behavior of least energy solutions to the Lane-Emden system near the critical hyperbola","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Seunghyeok Kim, Woocheol Choi","submitted_at":"2018-07-15T19:03:49Z","abstract_excerpt":"The Lane-Emden system is written as \\begin{equation*} \\begin{cases} -\\Delta u = v^p &\\text{in } \\Omega,\\\\ -\\Delta v = u^q &\\text{in } \\Omega,\\\\ u, v > 0 &\\text{in } \\Omega,\\\\ u = v = 0 &\\text{on } \\partial \\Omega \\end{cases} \\end{equation*} where $\\Omega$ is a smooth bounded domain in the Euclidean space $\\mathbb{R}^n$ for $n \\ge 3$ and $0< p< q <\\infty$. The asymptotic behavior of least energy solutions near the critical hyperbola was studied by Guerra \\cite{G} when $p \\geq 1$ and the domain is convex. In this paper, we cover all the remaining cases $p < 1$ and extend the results to any smoot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05596","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"}