Geodesic
On some problems of instability in semi-dynamical systems
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2021), pp. 39-45.

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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. 
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B. S. Kalitin. On some problems of instability in semi-dynamical systems. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2021), pp. 39-45. http://geodesic.mathdoc.fr/item/BGUMI_2021_1_a2/

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