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Title: Averaging for ordinary differential equations perturbed by a small parameter (English)
Author: Lakrib, Mustapha
Author: Kherraz, Tahar
Author: Bourada, Amel
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 141
Issue: 2
Year: 2016
Pages: 143-151
Summary lang: English
Category: math
Summary: In this paper, we prove and discuss averaging results for ordinary differential equations perturbed by a small parameter. The conditions we assume on the right-hand sides of the equations under which our averaging results are stated are more general than those considered in the literature. Indeed, often it is assumed that the right-hand sides of the equations are uniformly bounded and a Lipschitz condition is imposed on them. Sometimes this last condition is relaxed to the uniform continuity in the second variable uniformly with respect to the first one. In our results, we assume only that the right-hand sides of the equations are bounded by some locally Lebesgue integrable functions with the property that their indefinite integrals satisfy a Lipschitz-type condition. Also, we consider that they are only continuous in the second variable uniformly with respect to the first one. (English)
Keyword: ordinary differential equation
Keyword: method of averaging
MSC: 34C15
MSC: 34C29
MSC: 34K25
idZBL: Zbl 06587859
idMR: MR3499781
DOI: 10.21136/MB.2016.12
Date available: 2016-05-19T09:03:13Z
Last updated: 2020-07-01
Stable URL:
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