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Ukrainian Mathematical Journal

, Volume 58, Issue 5, pp 709–717 | Cite as

Partial asymptotic stability of abstract differential equations

  • A. L. Zuev
Article

Abstract

We consider the problem of partial asymptotic stability with respect to a continuous functional for a class of abstract dynamical processes with multivalued solutions on a metric space. This class of processes includes finite-and infinite-dimensional dynamical systems, differential inclusions, and delay equations. We prove a generalization of the Barbashin-Krasovskii theorem and the LaSalle invariance principle under the conditions of the existence of a continuous Lyapunov functional. In the case of the existence of a differentiable Lyapunov functional, we obtain sufficient conditions for the partial stability of continuous semigroups in a Banach space.

Keywords

Cauchy Problem Singular Point Classical Solution Asymptotic Stability Differential Inclusion 
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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. L. Zuev
    • 1
    • 2
  1. 1.Institute of Applied Mathematics and MechanicsUkrainian Academy of SciencesDonetsk
  2. 2.Technische Universitat IlmenauIlmenauGermany

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