### 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 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Differential and Integral Equations*,

*6*(1), 155-181.

**Perturbing semigroups by solving Stieltjes renewal equations.** / Diekmann, Odo; Gyllenberg, Mats; Thieme, Horst; Webb, Glenn.

Research output: Contribution to journal › Article

*Differential and Integral Equations*, vol. 6, no. 1, pp. 155-181.

}

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 -