Partial asymptotic stability of abstract differential equations

  • A. L. Zuev


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.
How to Cite
Zuev, A. L. “Partial Asymptotic Stability of Abstract Differential Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 5, May 2006, pp. 629–637,
Research articles