Averaging methods for piecewise-smooth ordinary differential equations

被引：1

作者：

Feckan, Michal ^{[1
,2
]}

Pacuta, Julius ^{[1
]}

Pospisil, Michal ^{[1
,2
]}

Vidlicka, Pavol ^{[1
]}

机构：

[1] Comenius Univ, Dept Math Anal & Numer Math, Fac Math Phys & Informat, Bratislava 84248, Slovakia

[2] Slovak Acad Sci, Inst Math, Stefanikova 49, Bratislava 81473, Slovakia

来源：

AIMS MATHEMATICS | 2019年 / 4卷 / 05期

关键词：

piecewise-smooth differential equations; averaging method; Filippov regularization;

D O I：

10.3934/math.2019.5.1466

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1466 / 1487

页数：22

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