Homogeneization Problems for Ordinary Differential Equations

G-convergence of differential equations is a weak form of convergence in which rather than structural coefficient convergence it is required only some form of convergence of the solutions. Hence this is a suitable form of convergence when coefficients oscillate faster and faster, as it happens when strips of different materials are placed one near to another. This limiting procedure is often called homogeneization and has important technological and physical meaning. In this paper we discuss homogeneization for ordinary differential equations, both when it happens with respect to time and when it happens with respect to the y variable (non-linear homogeneization). In this case the homogeneizated constant limit coefficient is given by the harmonic mea