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- W2556627417 abstract "In general this work consists of investigation of autonomous systems of dierential equations having Krasovsky property described in [1]. Briefly speaking a system satisfies Krasovsky property in the neighborhood of a bounded invariant set if all the solutions of this system leave this neighborhood with increasing or decreasing of time. Also, as it is derived from [1], Krasovsky property is equivalent to existing of a continuous function (so called Lyapunov - Krasovsky function) in this neighborhood, which changes monotonously along the solutions of the system, and as a consequence this property is kept under small C 0 perturbations of right part of the system. It was noted that for such a system there is a topological structure depending on behavior of the solutions in the neighborhood of invariant set only. So, first of all, it was an idea to define an index of the invariant set, something similar to rotation of vector field for example. Unfortunately it was not managed, i. e., it was not succeeded to define an index with “good” properties. Finally, this investigation has been pointed to the development of a criterion of nondisappearance of invariant sets satisfying Krasovsky property under C 0 perturbations of the right part of the system. In other words, it could happen that the invariant set disappears (i. e. becomes empty) for the perturbed system. At the same time, the Krasovsky property is still held for small C 0 perturbations. The developed criterion is based on structure of Lyapunov - Krasovsky function and allows to determine, if such a disappearance could happen." @default.
- W2556627417 created "2016-11-30" @default.
- W2556627417 creator A5073788938 @default.
- W2556627417 date "1999-01-01" @default.
- W2556627417 modified "2023-09-23" @default.
- W2556627417 title "A Criterion of Nondisappearance of Invariant Sets Satisfying Krasovsky Property under C 0 Perturbations of Right Part of the System." @default.
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