Twin semigroups and delay equations
In the standard theory of delay equations, the fundamental solution does not ‘live’ in the state space. To eliminate this age-old anomaly, we enlarge the state space. As a consequence, we lose the strong continuity of the solution operators and this, in turn, has as a consequence that the Riemann in...
Saved in:
| Published in: | Journal of Differential Equations Vol. 286; pp. 332 - 410 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Inc
15-06-2021
|
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In the standard theory of delay equations, the fundamental solution does not ‘live’ in the state space. To eliminate this age-old anomaly, we enlarge the state space. As a consequence, we lose the strong continuity of the solution operators and this, in turn, has as a consequence that the Riemann integral no longer suffices for giving meaning to the variation-of-constants formula. To compensate, we develop the Stieltjes-Pettis integral in the setting of a norming dual pair of spaces. Part I provides general theory, Part II deals with “retarded” equations, and in Part III we show how the Stieltjes integral enables incorporation of unbounded perturbations corresponding to neutral delay equations. |
|---|---|
| ISSN: | 0022-0396 1090-2732 |
| DOI: | 10.1016/j.jde.2021.02.052 |