Stability of solutions for nonlinear nonautonomous differential-delay equations in Hubert spaces

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Abstract

We consider nonlinear non-autonomous differential-delay equations having separated linear and sublinear parts. We assume that the Green functions of the linear part is selfadjoint and positive definite to obtain solution estimates, explicit conditions for the absolute stability, and input-output stability. Moreover, it is shown that the suggested conditions characterize the equations that satisfy the generalized Aizerman - Myshkis hypothesis.

Original languageEnglish
Pages (from-to)XCXCI-XCXCII
JournalElectronic Journal of Differential Equations
Volume2002
StatePublished - 1 Dec 2002

Keywords

  • Absolute stability
  • Aizerman-myshkis problem
  • Input-output stability
  • Nonlinear differential-delay equations in hilbert spaces

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