A class of abstract delay differential equations in the light of suns and stars

2019/01/31 by Sebastiaan G. Janssens, Janssens, Sebastiaan G.
Computer Science · Mathematics · #34K30 #47D06 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1901.11526

openalex publication_date 2019/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using dual perturbation theory in a non-sun-reflexive context, we establish a correspondence between 1. a class of nonlinear abstract delay differential equations (DDEs) with unbounded linear part and an unknown taking values in an arbitrary Banach space and 2. a class of abstract weak* integral equations of convolution type involving the sun-star adjoint of a translation-like strongly continuous semigroup. For this purpose we also characterize the sun dual of the underlying state space. More generally we consider bounded linear perturbations of an arbitrary strongly continuous semigroup and we comment on some implications for the particular case of abstract DDEs.

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