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Behavior of Trajectories of the Levinson-Smith Equation

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Abstract

The method of localization of invariant compact sets is used to study the properties of solutions of the Levinson-Smith equation with or without bounded disturbances. Necessary and sufficient conditions for the existence of localizing functions with a bounded universal section are obtained. Conditions for the existence of a bounded localizing set are established. The results are used to describe the solution behavior.

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Funding

This work was supported by the Russian Science Foundation, project no. 17-11-001220.

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Moscow, 105005, Russia

    A. P. Krishchenko

  2. Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, 119333, Russia

    A. P. Krishchenko

Authors
  1. A. P. Krishchenko
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Correspondence to A. P. Krishchenko.

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Russian Text © The Author(s), 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 11, pp. 1476–1484.

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Krishchenko, A.P. Behavior of Trajectories of the Levinson-Smith Equation. Diff Equat 55, 1431–1439 (2019). https://doi.org/10.1134/S001226611911003X

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  • DOI: https://doi.org/10.1134/S001226611911003X

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