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A class of abstract delay differential equations in the light of suns and stars. (arXiv:1901.11526v1 [math.DS])
来源于:arXiv
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. 查看全文>>