{"paper":{"title":"Blow-up analysis for nodal radial solutions in Moser-Trudinger critical equations in $R^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daisuke Naimen, Massimo Grossi","submitted_at":"2017-06-28T11:39:11Z","abstract_excerpt":"In this paper we consider nodal radial solutions $u_\\epsilon$ to the problem \\[ \\begin{cases} -\\Delta u=\\lambda ue^{u^2+|u|^{1+\\epsilon}}&\\text{ in }B,\\\\ u=0&\\text{ on }\\partial B. \\end{cases} \\] and we study their asymptotic behaviour as $\\epsilon\\searrow0$, $\\epsilon>0$. We show that when $u_\\epsilon$ has $k$ interior zeros, it exhibits a multiple blow-up behaviour in the first $k$ nodal sets while it converges to the least energy solution of the problem with $\\epsilon=0$ in the $(k+1)$-th one. We also prove that in each concentration set, with an appropriate scaling, $u_\\epsilon$ converges "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09223","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"}