This article is cited in 1 paper

Differential equations and Optimal control

On some problems of instability in semi-dynamical systems

B. S. Kalitin

Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

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 neighbourhood of positive Lagrange stable semi-trajectories; the space $X$ is asymptotically compact in some neighbourhood of $M$.

Keywords: semi-dynamical system; closed set; instability; Lyapunov function.

UDC: 517.938:925

Received: 31.01.2021

DOI: 10.33581/2520-6508-2021-1-39-45