{"paper":{"title":"Multiplicity of multi-bump type nodal solutions for a class of elliptic problems with exponential critical growth in $\\mathbb{R}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Denilson S. Pereira","submitted_at":"2014-12-13T10:07:24Z","abstract_excerpt":"In this paper, we establish the existence and multiplicity of multi-bump nodal solutions for the following class of problems $$ -\\Delta u+(\\lambda V(x)+1)u=f(u),~~\\mbox{in}~~\\mathbb{R}^2, $$ where $\\lambda\\in(0,\\infty)$, $f$ is a continuous function with exponential critical growth and $V:\\mathbb{R}^2\\to \\mathbb{R}$ is a continuous function verifying some hypotheses."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4219","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"}