An Averaging Theorem for Ordinary Differential Inclusions

Lakrib, Mustapha

Bull. Belg. Math. Soc. Simon Stevin, Volume 16 (2009) no. 1, p. 13-29 / Harvested from Project Euclid

Abstract

We consider the problem of application of the method of averaging to the asymptotic approximation of solutions of ordinary differential inclusions of the form $\dot x(t) \in f(t/\varepsilon,x(t))$. Our result is formulated in both classical mathematics and nonstandard analysis; its proof uses some methods of nonstandard analysis.

Published online : 2009-02-15
Classification: Averaging, Differential inclusions, Stroboscopic method, Nonstandard analysis, 34C29, 34A60, 34E10, 34E18

@article{1235574188,
     author = {Lakrib, Mustapha},
     title = {An Averaging Theorem for Ordinary Differential Inclusions},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {16},
     number = {1},
     year = {2009},
     pages = { 13-29},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1235574188}
}

Lakrib, Mustapha. An Averaging Theorem for Ordinary Differential Inclusions. Bull. Belg. Math. Soc. Simon Stevin, Volume 16 (2009) no. 1, pp.  13-29. http://gdmltest.u-ga.fr/item/1235574188/