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Averaging methods for piecewise-smooth ordinary differential equations

1 Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia
2 Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia

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

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