Time averaging for ordinary differential equations and retarded functional differential equations

Abstract : We prove averaging theorems for non-autonomous ordinary differential equations and retarded functional differential equations in the case where the vector fields are continuous in the spatial variable uniformly with respect to the time and the solution of the averaged system exists on some given interval. Our assumptions are weaker than those required in the results of the existing literature. Usually, we require that the non-autonomous differential equation and the autonomous averaged equation are locally Lipschitz and that the solutions of both equations exist on some given interval. Our results are formulated in classical mathematics. Their proofs use the stroboscopic method which is a tool of the nonstandard asymptotic theory of differential equations.
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Article dans une revue
Electronic Journal of Differential Equations, Texas State University, Department of Mathematics, 2010, 〈http://www.emis.de/journals/EJDE/Volumes/2010/40/lakrib.pdf〉
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https://hal.inria.fr/inria-00505283
Contributeur : Tewfik Sari <>
Soumis le : vendredi 23 juillet 2010 - 11:09:25
Dernière modification le : samedi 27 janvier 2018 - 01:31:49

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  • HAL Id : inria-00505283, version 1

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Mustapha Lakrib, Tewfik Sari. Time averaging for ordinary differential equations and retarded functional differential equations. Electronic Journal of Differential Equations, Texas State University, Department of Mathematics, 2010, 〈http://www.emis.de/journals/EJDE/Volumes/2010/40/lakrib.pdf〉. 〈inria-00505283〉

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