Stability of abstract nonlinear nonautonomous differential-delay equations with unbounded history-responsive operators

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4 Scopus citations

Abstract

We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.

Original languageEnglish
Pages (from-to)140-158
Number of pages19
JournalJournal of Mathematical Analysis and Applications
Volume308
Issue number1
DOIs
StatePublished - 1 Aug 2005

Keywords

  • Absolute stability
  • Abstract nonlinear differential-delay equations
  • Boundedness of solutions
  • Input-output stability
  • Lyapunov stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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