{"paper":{"title":"Lane Emden problems with large exponents and singular Liouville equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christopher Grumiau, Filomena Pacella, Massimo Grossi","submitted_at":"2012-09-07T13:42:50Z","abstract_excerpt":"We consider the Lane-Emden Dirichlet problem -\\Delta u = \\abs{u}^{p-1}u, in B, u =0, on \\partial B, where $p>1$ and $B$ denotes the unit ball in $\\IR^2$. We study the asymptotic behavior of the least energy nodal radial solution $u_p$, as $p\\rightarrow +\\infty$. Assuming w.l.o.g. that $u_p(0) < 0$, we prove that a suitable rescaling of the negative part $u_p^-$ converges to the unique regular solution of the Liouville equation in $\\IR^2$, while a suitable rescaling of the positive part $u_p^+$ converges to a (singular) solution of a singular Liouville equation in $\\IR^2$. We also get exact asy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1534","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"}