Partial asymptotic stability of abstract differential equations
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.
English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 5, pp 709-717.
Citation Example: Zuev A. L. Partial asymptotic stability of abstract differential equations // Ukr. Mat. Zh. - 2006. - 58, № 5. - pp. 629–637.