On some problems of instability in semi-dynamical systems

DOI: https://doi.org/10.33581/2520-6508-2021-1-39-45

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.

Author Biography

Boris S. Kalitine, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

PhD (physics and mathematics), docent; professor at the department of analytical economics and econometrics, faculty of economy

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Published
2021-04-12
Keywords: semi-dynamical system, closed set, instability, Lyapunov function
How to Cite
Kalitine, B. S. (2021). On some problems of instability in semi-dynamical systems. Journal of the Belarusian State University. Mathematics and Informatics, 1, 39-45. https://doi.org/10.33581/2520-6508-2021-1-39-45
Issue
No 1 (2021): Journal of the Belarusian State University. Mathematics and Informatics
Section
Differential Equations and Optimal Control

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