Abstract Delay Equations Inspired by Population Dynamics

Odo Diekmann () and Mats Gyllenberg ()
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Odo Diekmann: University of Utrecht, Department of Mathematics
Mats Gyllenberg: University of Helsinki, Rolf Nevanlinna Institute, Department of Mathematics and Statistics

A chapter in Functional Analysis and Evolution Equations, 2007, pp 187-200 from Springer

Abstract: Abstract In this short note we show that delay equations can be reformulated as abstract weak*-integral equations (AIE) involving dual semigroups, even in the case of infinite delay and/or when the solution takes values in a non-reflexive Banach space. The advantage is that for such (AIE) the standard local stability and bifurcation results are already available, see [8]. Our motivation derives from models of physiologically structured populations, as explained in more detail in [12].

Keywords: Delay equations; dual semigroup; sun-star-calculus; infinite delay; non-sun-reflexive case; principle of linearized stability; center manifold; Hopf bifurcation; physiologically structured populations (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7794-6_12

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DOI: 10.1007/978-3-7643-7794-6_12

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