{"paper":{"title":"Bounded solutions of finite lifetime to differential equations in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Helge Glockner, Rafael Dahmen","submitted_at":"2014-02-07T16:56:05Z","abstract_excerpt":"Consider a smooth vector field $f\\colon \\mathbb{R}^n\\to\\mathbb{R}^n$ and a maximal solution $\\gamma\\colon \\,]a,b[\\,\\to \\mathbb{R}^n$ to the ordinary differential equation $x'=f(x)$. It is a well-known fact that, if $\\gamma$ is bounded, then $\\gamma$ is a global solution, i.e., $\\,]a,b[\\,=\\mathbb{R}$. We show by example that this conclusion becomes invalid if $\\mathbb{R}^n$ is replaced with an infinite-dimensional Banach space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1692","kind":"arxiv","version":3},"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"}