{"paper":{"title":"Theory of well-posedness for delay differential equations via prolongations and $C^1$-prolongations: its application to state-dependent delay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Junya Nishiguchi","submitted_at":"2018-10-13T16:50:11Z","abstract_excerpt":"In this paper, we establish a theory of well-posedness for delay differential equations (DDEs) via notions of \\textit{prolongations} and \\textit{$C^1$-prolongations}, which are continuous and continuously differentiable extensions of histories to the right, respectively. In this sense, this paper serves as a continuation and an extension of the previous paper by this author (\\cite{Nishiguchi 2017}). The results in \\cite{Nishiguchi 2017} are applicable to various DDEs, however, the results in \\cite{Nishiguchi 2017} cannot be applied to general class of state-dependent DDEs, and its extendabilit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05890","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"}