TITLE

Partial asymptotic stability of abstract differential equations

AUTHOR(S)
Zuev, A. L.
PUB. DATE
May 2006
SOURCE
Ukrainian Mathematical Journal;May2006, Vol. 58 Issue 5, p709
SOURCE TYPE
Academic Journal
DOC. TYPE
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.
ACCESSION #
22642790

 

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