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A threshold state-dependent delayed functional equation arising from marine population dynamics: modelling and analysis

A threshold state-dependent delayed functional equation arising from marine population dynamics:... This paper deals with a functional state-dependent delayed equation in which the delay is implicitly defined by a threshold condition. The equation originates in a class of age-structured population models in which the passage of individuals through the different stages of their life cycle occurs when some magnitude reaches a threshold value. The work analyses local existence of solutions, global existence of nonnegative solutions and uniqueness for smooth initial data. Some partial results on existence and stability of nonnegative stationary solutions are established through a linearized equation. This linearization is constructed from a differential formulation of the problem which is not equivalent to the original one, and the mathematical analysis is carried out in the setting of the C 0 -semigroup theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

A threshold state-dependent delayed functional equation arising from marine population dynamics: modelling and analysis

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References (13)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer Basel AG
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-010-0075-x
Publisher site
See Article on Publisher Site

Abstract

This paper deals with a functional state-dependent delayed equation in which the delay is implicitly defined by a threshold condition. The equation originates in a class of age-structured population models in which the passage of individuals through the different stages of their life cycle occurs when some magnitude reaches a threshold value. The work analyses local existence of solutions, global existence of nonnegative solutions and uniqueness for smooth initial data. Some partial results on existence and stability of nonnegative stationary solutions are established through a linearized equation. This linearization is constructed from a differential formulation of the problem which is not equivalent to the original one, and the mathematical analysis is carried out in the setting of the C 0 -semigroup theory.

Journal

Journal of Evolution Equations – Springer Journals

Published: Nov 1, 2010

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