On some problems of instability in semi-dynamical systems

Abstract

The problem of instability of a closed positively invariant set M of a semi-dynamical system on an arbitrary metric space X is considered. The Lyapunov’s direct method for such problems has been developed quite completely in the case when M is compact and X is locally compact. In this article, we obtain sufficient conditions for instability in terms of Lyapunov functions in two situations: M has a neighborhood of positive Lagrange stable semi-trajectories; the space X is asymptotically compact in some neighborhood of M.

Keywords

• semi-dynamical system
• closed set
• instability
• lyapunov function