Geodesic
Time averaging for ordinary differential equations and retarded functional differential equations
Electronic journal of differential equations, Tome 2010 (2010)
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.
Classification : 34C29, 34C15, 34K25, 34E10, 34E18
Keywords: averaging, ordinary differential equations, stroboscopic method, retarded functional differential equations, nonstandard analysis 
@article{EJDE_2010__2010__a18,
     author = {Lakrib,  Mustapha and Sari,  Tewfik},
     title = {Time averaging for ordinary differential equations and retarded functional differential equations},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1201.34128},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a18/}
}
TY  - JOUR
AU  - Lakrib,  Mustapha
AU  - Sari,  Tewfik
TI  - Time averaging for ordinary differential equations and retarded functional differential equations
JO  - Electronic journal of differential equations
PY  - 2010
VL  - 2010
UR  - http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a18/
LA  - en
ID  - EJDE_2010__2010__a18
ER  - 
%0 Journal Article
%A Lakrib,  Mustapha
%A Sari,  Tewfik
%T Time averaging for ordinary differential equations and retarded functional differential equations
%J Electronic journal of differential equations
%D 2010
%V 2010
%U http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a18/
%G en
%F EJDE_2010__2010__a18
Lakrib,  Mustapha; Sari,  Tewfik. Time averaging for ordinary differential equations and retarded functional differential equations. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a18/