RENEWAL THEOREMS FOR LINEAR PERIODIC VOLTERRA INTEGRAL EQUATIONS.

Research output: Contribution to journalArticle

25 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)253-277
Number of pages25
JournalJournal of integral equations
Volume7
Issue number3
StatePublished - Nov 1984
Externally publishedYes

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Integral equations
Banach spaces

ASJC Scopus subject areas

  • Engineering(all)

Cite this

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

In: Journal of integral equations, Vol. 7, No. 3, 11.1984, p. 253-277.

Research output: Contribution to journalArticle

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