A necessary and sufficient condition for well-posedness of initial value problems of retarded functional differential equations

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We introduce the retarded functional differential equations (RFDEs) with general delay structure to treat various delay differential equations (DDEs) in a unified way and to clarify the delay structure in those dynamics. We are interested in the question as to which space of histories is suitable for the dynamics of each DDE, and investigate the well-posedness of the initial value problems (IVPs) of the RFDEs. A main theorem is that the IVP is well-posed for any “admissible” history functional if and only if the semigroup determined by the trivial RFDE x˙=0 is continuous. We clarify the meaning of the Hale–Kato axiom (Hale & Kato [12]) by applying this result to RFDEs with infinite delay. We also apply the result to DDEs with unbounded time- and state-dependent delays.

Original languageEnglish
Pages (from-to)3491-3532
Number of pages42
JournalJournal of Differential Equations
Volume263
Issue number6
DOIs
Publication statusPublished - 2017 Sep 15
Externally publishedYes

Keywords

  • Infinite delay
  • Retarded functional differential equations
  • State-dependent delay
  • Well-posedness of initial value problems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A necessary and sufficient condition for well-posedness of initial value problems of retarded functional differential equations'. Together they form a unique fingerprint.

Cite this