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)|
|Number of pages||25|
|Journal||Journal of integral equations|
|State||Published - Nov 1 1984|
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