{"paper":{"title":"Bubbling nodal solutions for a large perturbation of the Moser-Trudinger equation on planar domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Daisuke Naimen, Gabriele Mancini, Massimo Grossi","submitted_at":"2019-03-05T21:19:02Z","abstract_excerpt":"In this work we study the existence of nodal solutions for the problem $$ -\\Delta u = \\lambda u e^{u^2+|u|^p} \\text{ in }\\Omega, \\; u = 0 \\text{ on }\\partial \\Omega, $$ where $\\Omega\\subseteq \\mathbb R^2$ is a bounded smooth domain and $p\\to 1^+$. If $\\Omega$ is ball, it is known that the case $p=1$ defines a critical threshold between the existence and the non-existence of radially symmetric sign-changing solutions. In this work we construct a blowing-up family of nodal solutions to such problem as $p\\to 1^+$, when $\\Omega$ is an arbitrary domain and $\\lambda$ is small enough. As far as we kn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02060","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"}