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This article is cited in 3 scientific papers (total in 3 papers)
MATHEMATICS
Examples of differential systems with contrasting combinations of Lyapunov, Perron, and upper-limit properties
A.A. Bondarev, I. N. Sergeev Lomonosov Moscow State University
Abstract:
A number of examples of systems of differential equations are given that have, in a sense, opposite properties of stability or instability of various types: Lyapunov, Perron, and upper-limit. Specifically, all nonzero solutions of one of these systems tend to zero (with unlimited growth of time), nevertheless moving away from it at least once at a specific distance common for all the solutions. In another system, all nonzero solutions starting in a fixed neighborhood of zero tend to infinity in norm, while the other solutions, on the contrary, tend to zero.
Keywords:
differential system, Lyapunov stability, Perron stability, upper-limit stability, autonomous systems, nonlinear systems, asymptotic properties of solutions.
Citation:
A.A. Bondarev, I. N. Sergeev, “Examples of differential systems with contrasting combinations of Lyapunov, Perron, and upper-limit properties”, Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022), 25–29; Dokl. Math., 106:2 (2022), 322–325
Linking options:
https://www.mathnet.ru/eng/danma292 https://www.mathnet.ru/eng/danma/v506/p25
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Abstract page: | 79 | References: | 10 |
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