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Norm continuity and stability for a functional differential equation in Hilbert space

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
269
Issue
2
Identifiers
DOI: 10.1016/s0022-247x(02)00075-6
Disciplines
  • Mathematics

Abstract

Abstract A functional differential equation in Hilbert space with initial data on [− h,0] is considered. An unbounded operator A and a square integrable weight function are acting in the distributed delay term. For a not necessarily continuous weight function the norm continuity of the associated solution semigroup is established at every t> h. In the case that the spectrum of A is real and negative, the asymptotic stability of the solution is obtained.

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