scholarly journals Retarded resolvent operators for linear retarded functional differential equations in a Banach space

1994 ◽  
Vol 20 (2) ◽  
pp. 319-363
Author(s):  
Byong Mun KIM ◽  
Kunio TSURUTA
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Resolvent Operators ◽  
Retarded Functional Differential Equations ◽  
Functional Differential

scholarly journals Perturbation theory for dual semigroups II. Time-dependent perturbations in the sun-reflexive case

1988 ◽  
Vol 109 (1-2) ◽  
pp. 145-172 ◽  
Author(s):  
Ph. Clément ◽  
O. Diekmann ◽  
M. Gyllenberg ◽  
H. J. A. M. Heijmans ◽  
H. R. Thieme
Keyword(s):  
Banach Space ◽  
Functional Differential Equations ◽  
Time Dependent ◽  
Evolutionary System ◽  
Strongly Continuous Semigroups ◽  
Structured Population ◽  
Variation Of Constants ◽  
Retarded Functional Differential Equations ◽  
Functional Differential ◽  
Age Structured

SynopsisWe consider time-dependent perturbations of generators of strongly continuous semigroups on a Banach space. The perturbations map the Banach space into a bigger space, which is the second dual of the original space in a specific semigroup sense. Using the theory of dual semigroups we show that the solutions of a generalised variation-of-constants formuladefine an evolutionary system. We investigate continuity and differentiability propertiesof this evolutionary system and its dual system and examine in what sense the perturbed generator and its adjoint generate these evolutionary systems. It is shown that the results apply naturally to retarded functional differential equations and age structured population dynamics.

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