{"paper":{"title":"Existence of multi-bump solutions to biharmonic operator with critical exponential growth in $\\mathbb{R}^4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Al\\^annio B. N\\'obrega, Denilson S. Pereira","submitted_at":"2016-03-18T18:02:16Z","abstract_excerpt":"Using variational methods, we establish existence of multi-bump solutions for the following class of problems $$\n  \\left\\{\n  \\begin{array}{l}\n  \\Delta^2 u +(\\lambda V(x)+1)u = f(u), \\quad \\mbox{in} \\quad \\mathbb{R}^{4},\n  u \\in H^{2}(\\mathbb{R}^{4}),\n  \\end{array}\n  \\right.\n  $$ where $\\Delta^2$ is the biharmonic operator, $f$ is a continuous function with critical exponential growth and $V : \\mathbb{R}^4 \\rightarrow \\mathbb{R}$ is a continuous function verifying some conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05946","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"}