### Abstract

The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. Under only continuity assumptions on the density dependent death and tertility rates, it is shown that a global continuum of positive equilibria exists in a certain Banach space. This continuum connects from the trivial solution at n = 1 to the boundary of the domain on which the problem is posed. Results concerning the spectrum are given. In particular, some circumstances are described under which positive equilibria exist for all n values greater than the critical value n = 1.

Original language | English (US) |
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Pages (from-to) | 175-188 |

Number of pages | 14 |

Journal | Computers and Mathematics with Applications |

Volume | 11 |

Issue number | 1-3 |

DOIs | |

State | Published - Jan 1 1985 |

### ASJC Scopus subject areas

- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics