Differentiability of solutions of second-order functional differential equations with unbounded delay

Hernán R. Henríquez, CARLOS VASQUEZ EHRENFELD

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19 Scopus citations

Abstract

In this paper we study the differentiability of solutions of the second-order semilinear abstract retarded functional differential equation with unbounded delay, specially when the underlying space is reflexive or at least has the Radon-Nikodym property. We apply our results to characterize the infinitesimal generators of several strongly continuous semigroups of linear operators that arise in the theory of linear abstract retarded functional differential equations with unbounded delay on a phase space defined axiomatically.

Original languageEnglish
Pages (from-to)284-312
Number of pages29
JournalJournal of Mathematical Analysis and Applications
Volume280
Issue number2
DOIs
StatePublished - 15 Apr 2003

Keywords

  • Abstract Cauchy problem
  • Cosine functions of operators
  • Differentiability of solutions
  • Functional differential equations

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