## 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) |
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Pages (from-to) | 253-277 |

Number of pages | 25 |

Journal | Journal of integral equations |

Volume | 7 |

Issue number | 3 |

State | Published - Nov 1 1984 |

Externally published | Yes |

## ASJC Scopus subject areas

- Engineering(all)