{"paper":{"title":"Multiple blow-up phenomena for the sinh-Poisson equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Massimo Grossi","submitted_at":"2012-10-21T12:23:24Z","abstract_excerpt":"We consider the sinh-Poisson equation $$(P)_\\lambda\\quad -\\Delta u=\\la\\sinh u\\ \\hbox{in}\\ \\Omega,\\ u=0\\ \\hbox{on}\\ \\partial\\Omega,$$ where $\\Omega$ is a smooth bounded domain in $\\rr^2$ and $\\lambda$ is a small positive parameter.\n  If $0\\in\\Omega$ and $\\Omega$ is symmetric with respect to the origin, for any integer $k$ if $\\la$ is small enough, we construct a family of solutions to $(P)_\\la$ which blows-up at the origin whose positive mass is $4\\pi k(k-1)$ and negative mass is $4\\pi k(k+1).$\n  It gives a complete answer to an open problem formulated by Jost-Wang-Ye-Zhou in [Calc. Var. PDE (2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5719","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"}