### Abstract

Renewal theorems as they have been proved, e. g. , by W. Feller for scalar Volterra integral equations are extended to periodic Volterra integral equations in ordered Banach spaces. This permits to show that, in linear models, age-structured populations which are spatially distributed and live in a periodically changing environment asymptotically exhibit geometric growth and a stationary seasonal age-space distribution which is independent of the initial state of the population. The results are specialized to Volterra integral equations. Further, as a basis for nonlinear renewal theorems, the positive solutions of limiting Volterra integral equations are characterized.

Original language | English (US) |
---|---|

Pages (from-to) | 253-277 |

Number of pages | 25 |

Journal | Journal of integral equations |

Volume | 7 |

Issue number | 3 |

State | Published - Nov 1984 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Journal of integral equations*,

*7*(3), 253-277.

**RENEWAL THEOREMS FOR LINEAR PERIODIC VOLTERRA INTEGRAL EQUATIONS.** / Thieme, Horst.

Research output: Contribution to journal › Article

*Journal of integral equations*, vol. 7, no. 3, pp. 253-277.

}

TY - JOUR

T1 - RENEWAL THEOREMS FOR LINEAR PERIODIC VOLTERRA INTEGRAL EQUATIONS.

AU - Thieme, Horst

PY - 1984/11

Y1 - 1984/11

N2 - Renewal theorems as they have been proved, e. g. , by W. Feller for scalar Volterra integral equations are extended to periodic Volterra integral equations in ordered Banach spaces. This permits to show that, in linear models, age-structured populations which are spatially distributed and live in a periodically changing environment asymptotically exhibit geometric growth and a stationary seasonal age-space distribution which is independent of the initial state of the population. The results are specialized to Volterra integral equations. Further, as a basis for nonlinear renewal theorems, the positive solutions of limiting Volterra integral equations are characterized.

AB - Renewal theorems as they have been proved, e. g. , by W. Feller for scalar Volterra integral equations are extended to periodic Volterra integral equations in ordered Banach spaces. This permits to show that, in linear models, age-structured populations which are spatially distributed and live in a periodically changing environment asymptotically exhibit geometric growth and a stationary seasonal age-space distribution which is independent of the initial state of the population. The results are specialized to Volterra integral equations. Further, as a basis for nonlinear renewal theorems, the positive solutions of limiting Volterra integral equations are characterized.

UR - http://www.scopus.com/inward/record.url?scp=0021523081&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021523081&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 253

EP - 277

JO - Journal of integral equations

JF - Journal of integral equations

SN - 0163-5549

IS - 3

ER -