{"paper":{"title":"Analyticity and Nonanalyticity of Solutions of Delay-Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"John Mallet-Paret, Roger D. Nussbaum","submitted_at":"2013-05-02T21:06:14Z","abstract_excerpt":"We consider the equation $$ \\dot x(t)=f(t,x(t),x(\\eta(t))) $$ with a variable time-shift $\\eta(t)$. Both the nonlinearity $f$ and the shift function $\\eta$ are given, and are assumed to be analytic (that is, holomorphic) functions of their arguments. Typically the time-shift represents a delay, namely that $\\eta(t)=t-r(t)$ with $r(t)\\ge 0$. The main problem considered is to determine when solutions (generally $C^\\infty$ and often periodic solutions) of the differential equation are analytic functions of $t$; and more precisely, to determine for a given solution at which values of $t$ it is ana"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0579","kind":"arxiv","version":2},"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"}