Abstract
We develop a perturbation theory for strongly continuous semigroups and dual semigroups not based on perturbation of infinitesimal generators but on certain families of bounded linear operators describing the cumulative effect of the feedback. The theory extends the theory of perturbation of generators by bounded or relatively bounded linear operators. The theory is applied to problems of structured population dynamics which cannot, to the best of our knowledge, be treated using a more conventional perturbation theory.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 155-181 |
| Number of pages | 27 |
| Journal | Differential and Integral Equations |
| Volume | 6 |
| Issue number | 1 |
| State | Published - 1993 |
Fingerprint
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Perturbing semigroups by solving Stieltjes renewal equations. / Diekmann, Odo; Gyllenberg, Mats; Thieme, Horst; Webb, Glenn.
In: Differential and Integral Equations, Vol. 6, No. 1, 1993, p. 155-181.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Perturbing semigroups by solving Stieltjes renewal equations
AU - Diekmann, Odo
AU - Gyllenberg, Mats
AU - Thieme, Horst
AU - Webb, Glenn
PY - 1993
Y1 - 1993
N2 - We develop a perturbation theory for strongly continuous semigroups and dual semigroups not based on perturbation of infinitesimal generators but on certain families of bounded linear operators describing the cumulative effect of the feedback. The theory extends the theory of perturbation of generators by bounded or relatively bounded linear operators. The theory is applied to problems of structured population dynamics which cannot, to the best of our knowledge, be treated using a more conventional perturbation theory.
AB - We develop a perturbation theory for strongly continuous semigroups and dual semigroups not based on perturbation of infinitesimal generators but on certain families of bounded linear operators describing the cumulative effect of the feedback. The theory extends the theory of perturbation of generators by bounded or relatively bounded linear operators. The theory is applied to problems of structured population dynamics which cannot, to the best of our knowledge, be treated using a more conventional perturbation theory.
UR - http://www.scopus.com/inward/record.url?scp=84972525241&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84972525241&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84972525241
VL - 6
SP - 155
EP - 181
JO - Differential and Integral Equations
JF - Differential and Integral Equations
SN - 0893-4983
IS - 1
ER -