A functional analytic perspective to delay differential equations

Rainer Picard, Sascha Trostorff, Marcus Waurick

Research output: Contribution to journalArticle

3 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.
LanguageEnglish
Pages217-236
Number of pages20
JournalOperators and Matrices
Volume8
Issue number1
DOIs
Publication statusPublished - 31 Mar 2014

Fingerprint

Delay Differential Equations
Differential equation
Contraction Mapping
Functional Analysis
Causality
Real Line
Hilbert space
Banach space
Generalise
Operator
Theorem
Class
History

Keywords

  • ordinary differential equations
  • causality
  • memory
  • delay

Cite this

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A functional analytic perspective to delay differential equations. / Picard, Rainer; Trostorff, Sascha; Waurick, Marcus.

In: Operators and Matrices, Vol. 8, No. 1, 31.03.2014, p. 217-236.

Research output: Contribution to journalArticle

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