A Hilbert space perspective on ordinary differential equations with memory term

Anke Kalauch, Rainer Picard, Stefan Siegmund, Sascha Trostorff, Marcus Waurick

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25 Citations (Scopus)


We discuss ordinary differential equations with delay and memory terms in Hilbert spaces. By introducing a time derivative as a normal operator in an appropriate Hilbert space, we develop a new approach to a solution theory covering integro-differential equations, neutral differential equations and general delay differential equations within a unified framework. We show that reasonable differential equations lead to causal solution operators.
Original languageEnglish
Pages (from-to)369-399
Number of pages31
JournalJournal of Dynamics and Differential Equations
Issue number2
Early online date13 Mar 2014
Publication statusPublished - 30 Jun 2014


  • ordinary differential equations
  • causality
  • memory
  • delay

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