A functional analytic perspective to delay differential equations

Rainer Picard, Sascha Trostorff, Marcus Waurick

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We generalize the solution theory for a class of delay type differential equations developed in a previous paper, dealing with the Hilbert space case, to a Banach space setting. The key idea is to consider differentiation as an operator with the whole real line as the underlying domain as a means to incorporate pre-history data. We focus our attention on the issue of causality of the differential equations as a characterizing feature of evolutionary problems and discuss various examples. The arguments mainly rely on a variant of the contraction mapping theorem and a few well-known facts from functional analysis.
Original languageEnglish
Pages (from-to)217-236
Number of pages20
JournalOperators and Matrices
Volume8
Issue number1
DOIs
Publication statusPublished - 31 Mar 2014

Keywords

  • ordinary differential equations
  • causality
  • memory
  • delay

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