Abstract
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 language | English |
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Pages (from-to) | 369-399 |
Number of pages | 31 |
Journal | Journal of Dynamics and Differential Equations |
Volume | 26 |
Issue number | 2 |
Early online date | 13 Mar 2014 |
DOIs | |
Publication status | Published - 30 Jun 2014 |
Keywords
- ordinary differential equations
- causality
- memory
- delay