Eventual norm continuity for neutral semigroups on Banach spaces

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Abstract

In this paper we prove, under suitable hypotheses, eventually norm continuity and compactness of the solution semigroups of certain neutral differential equations in Banach spaces. Our approach is based on a general perturbation theorem obtained from closed-loop systems of infinite dimensional control systems with unbounded control and observation operators. In fact, the solution semigroup can be viewed as the semigroup of an appropriate closed-loop system in product state spaces.

Original languageEnglish
Pages (from-to)543-552
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Volume375
Issue number2
DOIs
Publication statusPublished - 15 Mar 2011

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Keywords

  • Banach space
  • Compactness
  • Neutral semigroup
  • Norm continuity
  • Perturbation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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