Averaging for ordinary differential equations perturbed by a small parameter
| Autor: | Amel Bourada, Mustapha Lakrib, Tahar Kherraz |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
lcsh:Mathematics
General Mathematics Mathematical analysis method of averaging ordinary differential equation lcsh:QA1-939 Lebesgue integration Lipschitz continuity Method of averaging symbols.namesake Uniform continuity Ordinary differential equation Bounded function symbols Uniform boundedness Differential algebraic equation Mathematics |
| Zdroj: | Mathematica Bohemica, Vol 141, Iss 2, Pp 143-151 (2016) |
| ISSN: | 2464-7136 0862-7959 |
| DOI: | 10.21136/mb.2016.12 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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