Averaging of quasidifferential equations with fast and slow variables (Q1288235)

The authors extend the averaging method for systems of differential equations with slow and fast variables proposed in [\textit{M. M. Khapaev} and \textit{O. P. Filatov}, Differ. Uravn. 19, No. 9, 1640-1643 (1983; Zbl 0539.34033)] to systems of quasidifferential equations. The quasidifferential equation of a metric space \(X\) is the equation \[ d\bigl(x(t+\Delta), g(\Delta, t, x)\bigr) = o(\Delta), \] where \(d\) is the metric. The averaging method, applied for studying the systems of quasidifferential equations, enables the authors to expose an estimate for an approximative solution to the system. Moreover, as a consequence, for systems of differential equations with multivalued right-hand sides, corresponding estimates are obtained.