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Averaging methods for piecewise-smooth ordinary differential equations

  • Received: 11 July 2019 Accepted: 30 August 2019 Published: 23 September 2019
  • MSC : 34A36, 34C29

  • The averaging method is developed for periodic piecewise-smooth systems. We discuss the behavior of solutions intersecting the discontinuity boundary and the problems it introduces. We illustrate these difficulties on specific examples. In the case of transversal and sliding solutions, we introduce conditions that allow us to prove averaging theorems for piecewise-smooth periodic differential equations.

    Citation: Michal Fečkan, Július Pačuta, Michal Pospíśil, Pavol Vidlička. Averaging methods for piecewise-smooth ordinary differential equations[J]. AIMS Mathematics, 2019, 4(5): 1466-1487. doi: 10.3934/math.2019.5.1466

    Related Papers:

  • The averaging method is developed for periodic piecewise-smooth systems. We discuss the behavior of solutions intersecting the discontinuity boundary and the problems it introduces. We illustrate these difficulties on specific examples. In the case of transversal and sliding solutions, we introduce conditions that allow us to prove averaging theorems for piecewise-smooth periodic differential equations.


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    [8] J. A. Sanders, F. Verhulst, J. Murdock, Averaging Methods in Nonlinear Dynamical Systems, 2 Eds, New York: Springer, 2007.
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  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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