{"paper":{"title":"Alternating sign multibump solutions of nonlinear elliptic equations in expanding tubular domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filomena Pacella, Monica Clapp, Nils Ackermann","submitted_at":"2012-10-16T01:48:30Z","abstract_excerpt":"Let $\\Gamma$ denote a smooth simple curve in $\\mathbb{R}^{N}$, $N\\geq2$, possibly with boundary. Let $\\Omega_{R}$ be the open normal tubular neighborhood of radius 1 of the expanded curve $R\\Gamma:=\\{Rx\\mid x\\in \\Gamma\\smallsetminus\\partial\\Gamma\\}$. Consider the superlinear problem $-\\Delta u+\\lambda u=f(u)$ on the domains $\\Omega_{R}$, as $R\\rightarrow \\infty$, with homogeneous Dirichlet boundary condition. We prove the existence of multibump solutions with bumps lined up along $R\\Gamma$ with alternating signs. The function $f$ is superlinear at 0 and at $\\infty$, but it is not assumed to be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4229","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"}