Grammel, G. Averaging of multivalued differential equations. (English) Zbl 1036.34013 Int. J. Math. Math. Sci. 2003, No. 25, 1615-1622 (2003). Here, the following nonlinear perturbed differential inclusion is investigated \[ z'(t)\in\varepsilon F(z(t),y(t)),\quad y'(t)\in G(y(t)), \] where \(\varepsilon >0\) is the perturbation parameter, \(t\in [0,T/\varepsilon]\), \(z\) is the slow motion and \(y\) the fast motion. Additionally, \(F\) and \(G\) are assumed to be Lipschitz continuous in Hausdorff sense, with compact, convex and nonempty values.The author shows that, under a transitivity condition on the fast subsystem, there exists an averaged system whose trajectories approximate, uniformly in Hausdorff sense, the slow trajectories of the original one. Moreover, the approximation is of order \(O(\varepsilon^{\frac{1}{3}})\), as \(\varepsilon\rightarrow 0\). Reviewer: Nikolaos G. Yannakakis (Athens) Cited in 2 Documents MSC: 34A60 Ordinary differential inclusions 34E15 Singular perturbations for ordinary differential equations 34C29 Averaging method for ordinary differential equations Keywords:Differential inclusions; slow and fast subsystem; averaging method; perturbed system; invariant measure; approximation order; multifunction; solution map; measurable selection PDFBibTeX XMLCite \textit{G. Grammel}, Int. J. Math. Math. Sci. 2003, No. 25, 1615--1622 (2003; Zbl 1036.34013) Full Text: DOI EuDML